4,014 results on '"bifurcations"'
Search Results
2. The dynamics about asteroid (162173) Ryugu.
- Author
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Fu, Xiaoyu, Soldini, Stefania, Ikeda, Hitoshi, Scheeres, Daniel J., and Tsuda, Yuichi
- Subjects
- *
THREE-body problem , *ORBITS (Astronomy) , *POLYHEDRA , *FAMILIES , *EQUILIBRIUM , *ASTEROIDS - Abstract
The dynamical environment around the asteroid (162173) Ryugu is analyzed in detail using a constant-density polyhedron model based on the measurements from the Hayabusa2 mission. Six exterior equilibrium points (EPs) are identified along the ridge line of Ryugu, and their topological classifications fall into two distinctive categories. The initial periodic orbit (PO) families are computed and analyzed, including distant retrograde/prograde orbit (DRO/DPO) families and fifteen PO families emanating from the exterior EPs. The fifteen PO families are further divided into three categories: seven converge to an EP, seven reach Ryugu's surface, and one exhibits cyclic behavior during its progression. The existence of initial PO families converging to an EP is analyzed using the bifurcation of a degenerate EP. Connection between these families and similar ones in the circular restricted three-body problem (CRTBP) is also examined. Bifurcated PO families are identified and computed from the initial PO families, including ten families from the DROs, fifteen from the DPOs, and twenty-five associated with the EPs. The bifurcated families are separately analyzed and categorized in terms of their corresponding initial families. Connections established by the same bifurcation points between different bifurcated families are identified. A comparison is made for the dynamical environments of Ryugu and Bennu to evaluate the similarities and differences in the evolution of EPs and the progression of PO families in top-shaped asteroids. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Prey group defense and hunting cooperation among generalist-predators induce complex dynamics: a mathematical study.
- Author
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Roy, Jyotirmoy, Dey, Subrata, Kooi, Bob W., and Banerjee, Malay
- Abstract
Group defense in prey and hunting cooperation in predators are two important ecological phenomena and can occur concurrently. In this article, we consider cooperative hunting in generalist predators and group defense in prey under a mathematical framework to comprehend the enormous diversity the model could capture. To do so, we consider a modified Holling-Tanner model where we implement Holling type IV functional response to characterize grazing pattern of predators where prey species exhibit group defense. Additionally, we allow a modification in the attack rate of predators to quantify the hunting cooperation among them. The model admits three boundary equilibria and up to three coexistence equilibrium points. The geometry of the nontrivial prey and predator nullclines and thus the number of coexistence equilibria primarily depends on a specific threshold of the availability of alternative food for predators. We use linear stability analysis to determine the types of hyperbolic equilibrium points and characterize the non-hyperbolic equilibrium points through normal form and center manifold theory. Change in the model parameters leading to the occurrences of a series of local bifurcations from non-hyperbolic equilibrium points, namely, transcritical, saddle-node, Hopf, cusp and Bogdanov-Takens bifurcation; there are also occurrences of global bifurcations such as homoclinic bifurcation and saddle-node bifurcation of limit cycles. We observe two interesting closed ‘bubble’ form induced by global bifurcations due to change in the strength of hunting cooperation and the availability of alternative food for predators. A three dimensional bifurcation diagram, concerning the original system parameters, captures how the alternation in model formulation induces gradual changes in the bifurcation scenarios. Our model highlights the stabilizing effects of group or gregarious behaviour in both prey and predator, hence supporting the predator-herbivore regulation hypothesis. Additionally, our model highlights the occurrence of “saltatory equilibria" in ecological systems and capture the dynamics observed for lion-herbivore interactions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. A geometrical theory of gliding motility based on cell shape and surface flow.
- Author
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Lettermann, Leon, Ziebert, Falko, and Schwarz, Ulrich S.
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CELL morphology , *CELL motility , *ANALYTICAL solutions , *SPOROZOITES , *TOXOPLASMOSIS - Abstract
Gliding motilityproceeds with little changes in cell shape and often results from actively driven surface flows of adhesins binding to the extracellular environment. It allows for fast movement over surfaces or through tissue, especially for the eukaryotic parasites from the phylum apicomplexa, which includes the causative agents of the widespread diseases malaria and toxoplasmosis. We have developed a fully three-dimensional active particle theory which connects the self-organized, actively driven surface flow over a fixed cell shape to the resulting global motility patterns. Our analytical solutions and numerical simulations show that straight motion without rotation is unstable for simple shapes and that straight cell shapes tend to lead to pure rotations. This suggests that the curved shapes of Plasmodium sporozoites and Toxoplasma tachyzoites are evolutionary adaptations to avoid rotations without translation. Gliding motility is also used by certain myxo- or flavobacteria, which predominantly move on flat external surfaces and with higher control of cell surface flow through internal tracks. We extend our theory for these cases. We again find a competition between rotation and translation and predict the effect of internal track geometry on overall forward speed. While specific mechanisms might vary across species, in general, our geometrical theory predicts and explains the rotational, circular, and helical trajectories which are commonly observed for microgliders. Our theory could also be used to design synthetic microgliders. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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5. How can we avoid the extinction of any species naturally? A mathematical model.
- Author
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Misra, A. K., Pal, Soumitra, and Kang, Yun
- Subjects
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BIOLOGICAL extinction , *TOP predators , *ALLEE effect , *PREDATION , *MATHEMATICAL models , *ENDANGERED species , *POPULATION density - Abstract
A large number of herbivorous mammals and reptiles in many terrestrial ecosystems across the globe are presently in the receiving end of extinction. Over-exploitation by its immediate predator and anthropogenic actions is one of the main reasons. Reintroduction of apex predator or top predator at some instances has proven to be a successful strategy in restoring ecological balance. In this paper, we conceptualize the role of top predator in enriching the density of vulnerable species of lower trophic level, with the help of mathematical modeling. First, the dynamical behavior of two species system (prey and mesopredator) is studied, where growth of prey is subject to strong Allee effect. Also, the cost of predation induced fear is incorporated in the growth term. Parametric regions, for which the species perceive extinction risk are analyzed and depicted numerically. We consider that whenever density of the vulnerable species reach a certain threshold, minimum viable population, top predator is introduced in the habitat. Our obtained results show that a species population can be restored from the verge of extinction to a stable state with much higher population density with the introduction of top predator and even it stabilizes an oscillatory system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Stability and bifurcations of a host–parasitoid model with general host escape function and general stocking upon parasitoids.
- Author
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Bešo, Emin, Drino, Džana, Kalabušić, Senada, Kovačević, D., and Pilav, Esmir
- Subjects
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LYAPUNOV exponents , *BIOLOGICAL extinction , *PARASITOIDS , *EQUILIBRIUM - Abstract
This paper analyzes the generalization of a model presented in J. Bektešević, V. Hadžiabdić, S. Kalabušić, M. Mehuljić and E. Pilav [Dynamics of a class of host–parasitoid models with external stocking upon parasitoids,
Adv. Differ. Equ. 2021 (31) (2021)]. The study explores the behavior of the solution near equilibrium points when the system has different outcomes, such as extinction, infinitely many exclusion points or unique exclusion and coexistence. We prove global stability for the extinction and host-exclusion equilibrium. We also investigate the non-hyperbolic case of parasitoid-exclusion equilibrium and delve deeper into the 1:1 resonance. The transcritical bifurcation occurs at the host-exclusion equilibrium, indicating a threshold for host population invasion through transcritical bifurcation. Moreover, the local dynamics around the coexisting equilibrium can be highly complex due to the appearance of the Neimark–Sacker and period-doubling bifurcations. We provide the explicit form of the first Lyapunov exponent for the Neimark–Sacker bifurcation. Through numerical examples, we illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]- Published
- 2024
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7. Singularities of 3D vector fields preserving the Martinet form.
- Author
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Anastassiou, S.
- Subjects
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VECTOR fields , *DIFFEOMORPHISMS - Abstract
We study the local structure of vector fields on that preserve the Martinet -form . We classify their singularities up to diffeomorphisms that preserve the form , as well as their transverse unfoldings. We are thus able to provide a fairly complete list of the bifurcations such vector fields undergo. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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8. Natural Convection Fluid Flow and Heat Transfer in a Valley-Shaped Cavity.
- Author
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Bhowmick, Sidhartha, Roy, Laxmi Rani, Xu, Feng, and Saha, Suvash C.
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RAYLEIGH number ,UNSTEADY flow ,PRANDTL number ,FLUID flow ,HEAT transfer ,NATURAL heat convection - Abstract
The phenomenon of natural convection is the subject of significant research interest due to its widespread occurrence in both natural and industrial contexts. This study focuses on investigating natural convection phenomena within triangular enclosures, specifically emphasizing a valley-shaped configuration. Our research comprehensively analyses unsteady, non-dimensional time-varying convection resulting from natural fluid flow within a valley-shaped cavity, where the inclined walls serve as hot surfaces and the top wall functions as a cold surface. We explore unsteady natural convection flows in this cavity, utilizing air as the operating fluid, considering a range of Rayleigh numbers from Ra = 10
0 to 108 . Additionally, various non-dimensional times τ, spanning from 0 to 5000, are examined, with a fixed Prandtl number (Pr = 0.71) and aspect ratio (A = 0.5). Employing a two-dimensional framework for numerical analysis, our study focuses on identifying unstable flow mechanisms characterized by different non-dimensional times, including symmetric, asymmetric, and unsteady flow patterns. The numerical results reveal that natural convection flows remain steady in the symmetric state for Rayleigh values ranging from 100 to 7 × 103 . Asymmetric flow occurs when the Ra surpasses 7 × 103 . Under the asymmetric condition, flow arrives in an unsteady stage before stabilizing at the fully formed stage for 7 × 103 < Ra < 107 . This study demonstrates that periodic unsteady flows shift into chaotic situations during the transitional stage before transferring to periodic behavior in the developed stage, but the chaotic flow remains predominant in the unsteady regime with larger Rayleigh numbers. Furthermore, we present an analysis of heat transfer within the cavity, discussing and quantifying its dependence on the Rayleigh number. [ABSTRACT FROM AUTHOR]- Published
- 2024
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9. Bifurcation and chaos in simple discontinuous systems separated by a hypersurface.
- Author
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Hosham, Hany A. and Alharthi, Thoraya N.
- Subjects
POINCARE maps (Mathematics) ,ORBITS (Astronomy) ,DYNAMICAL systems ,LINEAR systems ,BIFURCATION diagrams ,CHAOS synchronization - Abstract
This research focuses on a mathematical examination of a path to sliding period doubling and chaotic behaviour for a novel limited discontinuous systems of dimension three separated by a nonlinear hypersurface. The switching system is composed of dissipative subsystems, one of which is a linear systems, and the other is not linked with equilibria. The non-linear sliding surface is designed to improve transient response for these subsystems. A Poincare return map is created that accounts for ´ the existence of the hypersurface, completely describing each individual sliding period-doubling orbits that route to the sliding chaotic attractor. Through a rigorous analysis, we show that the presence of a nonlinear sliding surface and a set of such hidden trajectories leads to novel bifurcation scenarios. The proposed system exhibits period-m orbits as well as chaos, including partially hidden and sliding trajectories. The results are numerically verified through path-following techniques for discontinuous dynamical systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
10. Nonlinear motion cascade to chaos in a rotor system based on energy transfer.
- Author
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Zhao, Runchao, Xu, Yeyin, Jiao, Yinghou, Li, Zhitong, Chen, Zengtao, and Chen, Zhaobo
- Abstract
The nonlinear stiffness of a structure results in complex nonlinear dynamic behaviors and bifurcations of rotor systems. However, there still lacks of comprehensive studies on the bifurcation-induced motion to chaos of the nonlinear system. This study investigated the energy transfer during the motion evolution to chaos around bifurcations. In this paper, a flexible rotor system with nonlinear stiffness is established and the nonlinear responses under different parameter excitations are studied. We construct the energy trajectory in energy space and propose a bifurcation detection method based on generalized energy transfer for studying the evolution of motion cascades to chaos. The induction of period-doubling and period-halving bifurcation is revealed through the energy trajectory. The stability domains of the rotor system in different parameter planes are determined based on the Lyapunov stability criterion. A nonlinear rotor test platform is built and speed-up experiments are carried out to verify the proposed bifurcation detection method based on generalized energy transfer. These results indicate that the energy transfer is consistent with the switching of bifurcations. The sudden shift and fluctuation in the generalized energy amplitude correspond to period-doubling bifurcation and chaos, respectively. The generalized energy curves reveal the period-halving bifurcation, which cannot be observed in the speed-up test. This research and proposed method have potential for application in condition monitoring and bifurcation recognition during the operation of rotating machinery. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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11. Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response.
- Author
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Uddin, Md. Jasim, Santra, P. K., Sohel Rana, Sarker Md., and Mahapatra, G. S.
- Subjects
GOMPERTZ functions (Mathematics) ,STATE feedback (Feedback control systems) ,PREDATION ,BIFURCATION diagrams ,DISPLAY systems ,PSYCHOLOGICAL feedback - Abstract
This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Nonlinearity
- Author
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Roos, Michael and Roos, Michael
- Published
- 2024
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13. Bifurcations in Inertial Focusing of a Particle Suspended in Flow Through Curved Rectangular Ducts
- Author
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Valani, Rahil N., Harding, Brendan, Stokes, Yvonne M., and Awrejcewicz, Jan, editor
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- 2024
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14. Modelling Thermoelastic Damping in Nonlinear Plates with Internal Resonance
- Author
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Soni, Darshan, Pandey, Manoj, Bajaj, Anil, and Lacarbonara, Walter, Series Editor
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- 2024
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15. Computational Investigation on the Empirical Relation of Murray’s Law
- Author
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Singhal, Mudrika, Gupta, Raghvendra, Chaari, Fakher, Series Editor, Gherardini, Francesco, Series Editor, Ivanov, Vitalii, Series Editor, Haddar, Mohamed, Series Editor, Cavas-Martínez, Francisco, Editorial Board Member, di Mare, Francesca, Editorial Board Member, Kwon, Young W., Editorial Board Member, Trojanowska, Justyna, Editorial Board Member, Xu, Jinyang, Editorial Board Member, Singh, Krishna Mohan, editor, Dutta, Sushanta, editor, Subudhi, Sudhakar, editor, and Singh, Nikhil Kumar, editor
- Published
- 2024
- Full Text
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16. Synchronous Activity in Small Ensembles of Inhibitory Coupled Phi-Neurons
- Author
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Korotkov, Alexander, Emelin, Artyom, Levanova, Tatiana, Osipov, Grigory, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Balandin, Dmitry, editor, Barkalov, Konstantin, editor, and Meyerov, Iosif, editor
- Published
- 2024
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17. New Characteristics of Blue Self-pulsating InGaN Lasers
- Author
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Grigoriev, Eugeniu, Rusu, Spiridon, Tronciu, Vasile, Magjarević, Ratko, Series Editor, Ładyżyński, Piotr, Associate Editor, Ibrahim, Fatimah, Associate Editor, Lackovic, Igor, Associate Editor, Rock, Emilio Sacristan, Associate Editor, Sontea, Victor, editor, Tiginyanu, Ion, editor, and Railean, Serghei, editor
- Published
- 2024
- Full Text
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18. Locating Period Doubling and Neimark-Sacker Bifurcations in Parametrically Excited Rotors on Active Gas Foil Bearings
- Author
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Dimou, Emmanouil, Gavalas, Ioannis, Dohnal, Fadi, Chasalevris, Athanasios, Ceccarelli, Marco, Series Editor, Agrawal, Sunil K., Advisory Editor, Corves, Burkhard, Advisory Editor, Glazunov, Victor, Advisory Editor, Hernández, Alfonso, Advisory Editor, Huang, Tian, Advisory Editor, Jauregui Correa, Juan Carlos, Advisory Editor, Takeda, Yukio, Advisory Editor, Chu, Fulei, editor, and Qin, Zhaoye, editor
- Published
- 2024
- Full Text
- View/download PDF
19. Complex Stable and Unstable Subharmonic Vibrations of a Nonlinear Brush-Seal Rotor System
- Author
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Ma, Wenbo, Xu, Yeyin, Jiao, Yinghou, Chen, Zhaobo, Ceccarelli, Marco, Series Editor, Agrawal, Sunil K., Advisory Editor, Corves, Burkhard, Advisory Editor, Glazunov, Victor, Advisory Editor, Hernández, Alfonso, Advisory Editor, Huang, Tian, Advisory Editor, Jauregui Correa, Juan Carlos, Advisory Editor, Takeda, Yukio, Advisory Editor, Chu, Fulei, editor, and Qin, Zhaoye, editor
- Published
- 2024
- Full Text
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20. Complex dynamics in a two species system with Crowley–Martin response function: Role of cooperation, additional food and seasonal perturbations.
- Author
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Mondal, Bapin, Thirthar, Ashraf Adnan, Sk, Nazmul, Alqudah, Manar A., and Abdeljawad, Thabet
- Subjects
- *
PREDATION , *SEASONS , *COOPERATION , *SYSTEM dynamics , *SPECIES - Abstract
This research article investigates the interaction between prey and a generalist predator, considering the effect of hunting cooperation. The predator–prey interaction is modeled using a predator dependent functional response, specifically the Crowley–Martin type. System's dynamics are explored using both analytical and numerical techniques. Feasible equilibria are analyzed, and their local stability is determined. Various bifurcations in the system are explored, and one-and two-parameter bifurcation structures are constructed to unveil complex dynamical behaviors. Our findings reveal that both prey and predator face extinction when the predator growth rate from alternative food sources exceeds certain threshold values. However, prey extinction is driven by the higher levels of hunting cooperation among predators, while the availability of external food sources enhances the system's stability and persistence. Furthermore, we enhance the model by introducing seasonal perturbations, acknowledging the influence of seasonal variations on ecological parameters. The system exhibits diverse patterns in response to seasonality, contributing to a deeper understanding of the dynamics in predator–prey interactions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. A Novel Fractional-Order Cascade Tri-Neuron Hopfield Neural Network: Stability, Bifurcations, and Chaos.
- Author
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Kumar, Pushpendra, Lee, Tae H., and Erturk, Vedat Suat
- Abstract
In this paper, we propose a novel Caputo-type fractional-order cascade tri-neuron Hopfield neural network (HNN) taking no connection between the first and third neuron. We analyse the symmetry and dissipativity of the system using divergence and transformations. The stability of the equilibrium points is checked by fixing the synaptic weights. To further analyse the dynamics of the HNN system, we derive a numerical solution by using the Adams–Bashforth–Moulton method along with its stability analysis. We performed several graphical simulations, considering two synaptic weights as adjustable variables, and explored the fact that the HNN system shows various periodic and chaotic attractors. The reason for proposing a fractional-order HNN is that such a system has limitless memory, which can improve the system’s controllability for a wide range of real-world phenomena with important applications. Also, the proposed fractional-order HNN shows better convergence compared to the integer-order case. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Bifurcation and chaos in simple discontinuous systems separated by a hypersurface
- Author
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Hany A. Hosham and Thoraya N. Alharthi
- Subjects
discontinuous systems ,bifurcations ,period-doubling ,sliding mode ,chaos ,Mathematics ,QA1-939 - Abstract
This research focuses on a mathematical examination of a path to sliding period doubling and chaotic behaviour for a novel limited discontinuous systems of dimension three separated by a nonlinear hypersurface. The switching system is composed of dissipative subsystems, one of which is a linear systems, and the other is not linked with equilibria. The non-linear sliding surface is designed to improve transient response for these subsystems. A Poincaré return map is created that accounts for the existence of the hypersurface, completely describing each individual sliding period-doubling orbits that route to the sliding chaotic attractor. Through a rigorous analysis, we show that the presence of a nonlinear sliding surface and a set of such hidden trajectories leads to novel bifurcation scenarios. The proposed system exhibits period-m orbits as well as chaos, including partially hidden and sliding trajectories. The results are numerically verified through path-following techniques for discontinuous dynamical systems.
- Published
- 2024
- Full Text
- View/download PDF
23. Local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors.
- Author
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Yang, Qing-Rui, Li, Xian-Feng, Yang, Zhe, and Leung, Andrew Y.-T.
- Subjects
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INVARIANT manifolds , *SIGNAL filtering , *ORBITS (Astronomy) , *BIFURCATION diagrams , *GLOBAL analysis (Mathematics) - Abstract
The paper devotes to the synthesis of local and global analysis of a discrete model describing the second-order digital filter with nonlinear signal processors. The discrete model gives rise to a two-dimensional non-invertible map, whose basins of attraction have complicated topological structures due to the intrinsic multi-stability. The influences of joint parameters on the local dynamics are presented in great details. Both theoretical and numerical results are plotted on the two-dimensional parametric planes. To show more detailed bifurcation structure, the isoclines are extended to higher periodic orbits for detecting the cusps of resonant entrainments. Invariant manifolds and critical curves are employed to illustrate the global dynamics of the model vividly. The tangency and intersections of invariant manifolds expound the process of erosions of basins of attraction. The global bifurcations of basins of attraction are deduced dynamically by critical curves. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Nonlinear dynamics and game-theoretic modeling in economics and finance.
- Author
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Bischi, Gian Italo, Baiardi, Lorenzo Cerboni, Lamantia, Fabio, and Radi, Davide
- Subjects
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DISCRETE-time systems , *SYSTEM dynamics , *ECONOMICS education , *DIFFERENTIAL games - Abstract
In this foreword to the Special Issue "Nonlinear dynamics and game-theoretical modeling in economics and finance" we review the contributions in the issue highlighting the economic results and the connections with aspects of dynamic analysis. Indeed, the common theme of the contributions is the focus on system dynamics and the latest analytical techniques. This issue is devoted to celebrating the 70th birthday of Professor Laura Gardini, who inspired a generation of scholars in the study of discrete-time systems and global methods of analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Modelling the dynamics of product adoption and abandonment.
- Author
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Kong, Lingju
- Subjects
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PRODUCT elimination , *HOPF bifurcations , *DIFFERENTIAL equations , *MASS media , *COMPUTER simulation - Abstract
We introduce a new compartmental differential equation model to examine the dynamics of user adoption and abandonment within a product context. This model features a nonlinear adoption rate and encompasses two distinct abandonment dynamics: infectious abandonment stemming from interactions among current and past users, and non-infectious abandonment induced by mass media, advertisements or the emergence of new products. Our exploration encompasses discussions on the existence and stability of model equilibria, as well as the derivation of a critical threshold quantity that regulates the model dynamics. Additionally, we establish criteria for backward and forward bifurcations and various forms of Hopf bifurcation. Detailed scrutiny of an associated optimal control problem is undertaken, starting with the establishment of the existence of an optimal control pair, followed by the determination of the requisite system conditions for this control pair. Extensive numerical simulations are conducted to validate the theoretical findings. Finally, we showcase the model's efficacy by fitting it to historical data on Facebook's daily active users, employing the derived parameter values to predict future user counts. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. STABILITY AND BIFURCATION OF A PREDATOR–PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS.
- Author
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XIA, YUE, HUANG, XINHAO, CHEN, FENGDE, and CHEN, LIJUAN
- Subjects
- *
ANTIPREDATOR behavior , *PREDATION , *HOPF bifurcations , *POPULATION density , *CUSP forms (Mathematics) , *EQUILIBRIUM - Abstract
In this paper, a predator–prey system with multiple anti-predator behaviors is developed and studied, where not only the prey may spread between patches but also the fear effect and counter-attack behavior of the prey are taken into account. First, the stability and existence of coexistence equilibria are presented. The unique positive equilibrium may be a saddle-node or a cusp of codimension 2. Then, various transversality conditions of bifurcations such as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are obtained. Moreover, compared with a single strategy, the multiple anti-predator strategies are more beneficial to the persistence and the population density of prey. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Fractional-Order Modeling and Nonlinear Dynamic Analysis of Forward Converter.
- Author
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Wang, Xiaogang and Zhang, Zetian
- Subjects
- *
NONLINEAR analysis , *HARDWARE-in-the-loop simulation , *DYNAMIC models , *FRACTIONAL calculus , *PREDICTION models , *BIFURCATION diagrams , *OSCILLATIONS - Abstract
To accurately investigate the nonlinear dynamic characteristics of a forward converter, a fractional-order state-space averaged model of a forward converter in continuous conduction mode (CCM) is established based on the fractional calculus theory. And nonlinear dynamical bifurcation maps which use PI controller parameters and a reference current as bifurcation parameters are obtained. The nonlinear dynamic behavior is analyzed and compared with that of an integral-order forward converter. The results show that under certain operating conditions, the fractional-order forward converter exhibits bifurcations characterized by low-frequency oscillations and period-doubling as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the forward converter. The stable zone of the fractional-order forward converter is larger than that of the integral-order one. Therefore, the circuit struggles to enter states of bifurcation and chaos. The stability domain for low-frequency oscillations and period-doubling bifurcations can be accurately predicted by using a small signal model and a predictive correction model of the fractional-order forward converter, respectively. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Period-1 Motions and Bifurcations of a 3D Brushless DC Motor System with Voltage Disturbance.
- Author
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Chen, Bin, Xu, Yeyin, Jiao, Yinghou, and Chen, Zhaobo
- Subjects
BRUSHLESS electric motors ,NONLINEAR dynamical systems ,VOLTAGE ,FOURIER series ,ANALYTICAL solutions ,DYNAMIC balance (Mechanics) - Abstract
In this paper, the nonlinear dynamic system of a brushless DC motor with voltage disturbance is studied analytically via a generalized harmonic balance method. A truncated Fourier series with time-varying coefficients is utilized to represent the analytical variations of nonlinear currents and voltages within this dynamic system. Bifurcations of periodic currents and voltages are obtained, and their stability is discussed through eigenvalue analysis. The frequency–amplitude characteristics of periodic currents and voltages exhibit complexity in the frequency domain. Comparative illustrations are provided to contrast the analytical solutions with numerical outcomes for periodic currents and voltages. These analytical findings can be effectively employed for controlling the brushless DC motors experiencing voltage disturbances. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Exploring Kinematic Bifurcations and Hinge Compliance for In‐Hand Manipulation: How Could Thick‐Panel Origami Contribute?
- Author
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Liu, Chenying, He, Liang, Wang, Sihan, Williams, Albert, You, Zhong, and Maiolino, Perla
- Subjects
ORIGAMI ,TACTILE sensors ,HINGES - Abstract
Origami‐inspired mechanisms have found significant applications in end effector design. So far, the exploration of thick‐panel origami has been relatively limited, but it is worth noting that the incorporation of rigid thick panels can introduce unique mechanical properties, showcasing great potential in addressing manipulation challenges. Our previous work has developed a gripper from thick‐panel waterbomb origami, which can pick up a variety of daily objects. Based on the same prototype, this article extends the gripper's function from grasping to in‐hand manipulation, which is attributed to the kinematic bifurcations and compliance of thick‐panel origami. A kinematic study is carried out to investigate the gripper's bifurcated motion modes. The hinge compliance is also taken into account to enhance the gripper's motion dexterity. Theoretical analysis and experiments are conducted to demonstrate both features, thereby paving the foundation for achieving dexterous motions with a simplified control strategy. Aided by a differential mechanism, the gripper can effectively interact with objects with the actuation inputs from only two motors. Objects including balls, cuboids, and cones are explored for in‐hand manipulation under different motion modes, showing varied trajectories. With the integration of tactile sensors at the fingertips, we have also revealed the gripper's potential for classification tasks. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Nonlinear dynamic analysis of a spring coupled double beam based piezoelectric energy harvester under parametric base excitation.
- Author
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Roy, Ranit and Dwivedy, Santosha Kumar
- Abstract
AbstractThis paper proposes a base excited, spring coupled double cantilever beam with attached tip mass based piezoelectric energy harvester. The dimensions of the beams are so chosen that the system experiences 1:1 internal resonance. The governing coupled electro-mechanical equations of motion of the system are obtained by using the Lagrange principle which is reduced to the temporal form by using generalized Galerkin’s method. The governing temporal equations of motion are in the form of that of a parametrically excited coupled system with geometric and inertial nonlinearities. These nonlinear equations are solved using the method of multiple scales and the results are compared with those solved by numerical method (4th order Runge Kutta method) for principal parametric resonance conditions. Parametric studies are conducted by varying the tip masses of the beams, coupled spring stiffness, load resistance, external excitation frequency and excitation amplitude. Results show that by introducing spring coupling, the system operational frequency range increases significantly and also energy transfer process takes place due to the internal resonance. Significant enhancement of voltage and power are observed in the present work in comparison to the earlier studied equivalent single beam-based energy harvester. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. Fifth-order evolution equation for a liquid film with odd viscosity.
- Author
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Zakaria, Kadry and Alsharif, Abdullah M.
- Subjects
- *
LIQUID films , *NONLINEAR wave equations , *VISCOSITY , *FILM flow , *THIN films , *EVOLUTION equations , *WAVE equation - Abstract
A fifth-order nonlinear wave equation (generalized Korteweg–deVries equation) that arises in the theory of thin liquid films is introduced with the odd viscosity by the long-wave approximation regime. The presence of the odd viscosity is considered to be a non-dissipative factor in the evolution of the film flow. Sinusoidal and travelling waves arise in systems with non dissipation and instability. The introduced wave equation includes quadratic and cubic nonlinearities. The linear instability of sinusoidal waves is analyzed. The stability and bifurcation of travelling waves are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Complex behaviors and various soliton profiles of (2+1)-dimensional complex modified Korteweg-de-Vries Equation.
- Author
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ur Rahman, Mati, Karaca, Yeliz, Sun, Mei, Baleanu, Dumitru, and Alfwzan, Wafa F.
- Subjects
- *
RUNGE-Kutta formulas , *NONLINEAR equations , *CHAOS theory , *DYNAMICAL systems , *EQUATIONS , *NONLINEAR dynamical systems - Abstract
Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution's stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Dynamics of a prey–predator model with reproductive Allee effect for prey and generalist predator.
- Author
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Manna, Kalyan and Banerjee, Malay
- Abstract
Generalist predation generally stabilizes the prey–predator dynamics since a generalist predator utilizes a variety of food sources to survive and shows prey-switching behavior at low focal prey density by reducing the predation pressure. On the other hand, the presence of Allee effect can potentially lead to a fairly complex prey–predator dynamics including the suppression of "the paradox of enrichment". In this paper, we explore the combined influence of reproductive Allee effect in prey growth and generalist predation on the resulting temporal as well as spatio-temporal dynamics. The temporal model mainly exhibits bistability in terms of stable equilibria. For the corresponding spatio-temporal model, we perform detailed theoretical analysis regarding the non-existence and existence of spatially heterogeneous steady states, and also provide conditions for Turing instability. The spatio-temporal model mainly exhibits stationary patterns and traveling wave solutions apart from the usual spatially homogeneous solutions. Our study reveals that oscillatory dynamics is less probable in the presence of abundant alternative food sources to predator population. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting.
- Author
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Mulugeta, Biruk Tafesse, Ren, Jingli, Yuan, Qigang, and Yu, Liping
- Subjects
- *
HOPF bifurcations , *COMPUTER simulation , *EQUILIBRIUM - Abstract
In this paper, we consider a predator–prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Dynamics of a nonlinear vibration absorption system with time delay.
- Author
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Mao, Xiaochen and Ding, Weijie
- Abstract
This paper reveals the dynamical responses of a time-delayed nonlinear vibration absorption system under harmonic excitation. The slow and fast dynamics of the forced system are analyzed by using complex averaging method. The curves of saddle-node bifurcation and Hopf bifurcation are given. Afterward, the analytical expressions and properties of slow invariant manifold are explored. The existence of strongly modulated response is determined by discussing the geometry of the slow invariant manifold. Furthermore, abundant and interesting behaviors are observed numerically and these phenomena reach a good agreement with theoretical analysis. The results show that time delay control plays important roles in the vibration reduction performance and can regulate the response regimes, such as the generation and transition of periodic orbits and quasi-periodic solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. Dynamics of chains of a large number of fully coupled oscillators, as well as oscillators with one-way and two-way delay couplings
- Author
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S.A. Kashchenko
- Subjects
Chains one-way and two-way couplings ,Bifurcations ,Stability ,Quasinormal forms ,Delay ,Dynamics ,Applied mathematics. Quantitative methods ,T57-57.97 - Abstract
This articles considers chains consisting of identical nonlinear equations of second order with couplings in linear elements. It is assumed that there is a large delay in the coupling elements. Moreover, we assume that the chain possesses a large number of elements. Therefore, instead of the original system with many elements, we can study a second order nonlinear integro-differential equation with periodic boundary conditions. The main study is focused on the local dynamics of chains with one-sided, two-sided couplings, as well as fully coupled chains. Also, we study the stability of equilibrium states and identify the critical cases. The condition of a sufficiently large delay helps to determine the parameters for the implementation of critical cases explicitly. Our methodology is based on the infinite-dimensional normalisation method proposed by the author, namely the method of quasinormal forms. We construct quasinormal forms for the chains under consideration that determine the asymptotics of the leading terms of the asymptotic expansions of the solutions to the original system.
- Published
- 2024
- Full Text
- View/download PDF
37. Effect of fear with saturated fear cost and harvesting on aquatic food chain model (plankton–fish model) in the presence of nanoparticles.
- Author
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Rashi, Singh, Harendra Pal, and Singh, Suruchi
- Subjects
- *
BIOLOGICAL extinction , *NUTRIENT cycles , *ECOSYSTEM health , *ALGAL blooms , *BIFURCATION diagrams - Abstract
Studying the interplay of phytoplankton–zooplankton–fish (PP–ZP–F) in an aquatic system is crucial for better understanding of nutrient cycling, assessing ecosystem health, predicting and mitigating harmful algal blooms, and managing fisheries in the water bodies. In order to investigate the effectiveness of nanoparticles (NPs), fear, and harvesting, this paper focuses on exploring the dynamics of a food chain model among PP–ZP–F species. We consider the fear of fish on zooplankton species (which reduces the reproduction rate of ZPs) with saturated fear cost in the presence of nanoparticles (NPs) and harvesting in fish. The system dynamics are studied from the viewpoint of proving positivity, boundedness, and uniqueness, followed by analysing the existence and local stability of biologically feasible equilibria. Conditions for the global stability of the interior equilibrium point are also found. Furthermore, we established the transversality conditions for the occurrence of Hopf, transcritical, and saddle–node bifurcations. To validate our theoretical results, we made numerous phase portraits, time-series graphs, tables showing the extinction of species, and bifurcation diagrams. It is numerically observed that increasing the contact rate of NPs with PPs makes the system stable from chaos, and further increase of contact rate may lead to extinction. Chaos at a low contact rate can also be managed by increasing the fear level, and the chaotic behaviour at a low fear level can again be controlled by enhancing the harvesting of fish species. Over-exploitation may result in the extinction of fish, whereas fear may promote coexistence, stability, and long-term survival of the species. Increased saturated fear cost can make the system chaotic from stable dynamics. Therefore, the theoretical as well as numerical findings of our paper may be of great interest in estimating the behaviour of aquatic systems biologically and practically. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Dynamics of a stockless market through piecewise smooth models.
- Author
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Molina-Díaz, Oscar Emilio, Olivar-Tost, Gerard, and Sotelo-Castelblanco, Deissy Milena
- Subjects
- *
ORDINARY differential equations , *VECTOR fields , *MATHEMATICAL analysis , *DYNAMICAL systems , *SMOOTHNESS of functions - Abstract
Markets play a crucial role in the economic activity of any country, serving as fundamental drivers of growth, development, and employment. Given their significance, understanding the dynamics of markets is essential. In this study, we present a mathematical model to characterize the behavior of a stockless market. The model is formulated using a system of ordinary differential equations defined with piecewise smooth functions. We conduct a mathematical analysis of the model, particularly focusing on the behavior of trajectories as they approach switching surfaces using Filippov's analysis. Furthermore, we provide numerical simulations to visually illustrate the model's dynamics and a insights a brief study of bifurcations is done. • A detailed description of the mathematical modeling of stockless markets is provided. • The dynamics are described by a system of smooth piecewise differential equations. • Switching surfaces are incorporated, dividing the state space into regions. • Sliding points are determined on these surfaces, defining a Filippov vector field. • A brief study of bifurcations is also conducted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Solutions of the equation an+(an-1+⋯(a2+(a1+xr1)r2)⋯)rn=bx
- Author
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Panazzolo, Daniel
- Published
- 2024
- Full Text
- View/download PDF
40. Chaos emergence and dissipation in a three-species food web model with intraguild predation and cooperative hunting
- Author
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Nazmul Sk, Bapin Mondal, Abhijit Sarkar, Shyam Sundar Santra, Dumitru Baleanu, and Mohamed Altanji
- Subjects
food web ,intraguild predation ,hunting cooperation ,chaos ,stability ,bifurcations ,Mathematics ,QA1-939 - Abstract
We explore the dynamics of a three-species Lotka-Volterra model incorporating intraguild (IG) predation. The model encompasses interactions between a basal prey, intraguild prey and omnivorous top/intraguild predator. These interactions are characterized by linear functional responses, while considering intraspecific competition and cooperative hunting dynamics. The study involves a comprehensive stability of different steady states and bifurcation analysis. Bifurcation structures unveil shifts in equilibrium stability and the emergence of new equilibrium states. Investigation into dynamics around the coexistence equilibrium highlights diverse behaviors, including stable coexistence, oscillations and chaos. Furthermore, exploration of species' densities under parameter variations uncovers distinct patterns, ranging from stability to chaos. Incorporating the concept of hunting cooperation among IG predators and IG prey can lead to the emergence or suppression of chaotic oscillations, respectively. Additionally, we observe that lower consumption rate of IG predator and cooperation of IG predator helps the system to keep in a stable state position.
- Published
- 2024
- Full Text
- View/download PDF
41. Steady state periodic response of truncated conical shell undergoing large amplitude vibration.
- Author
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Parvez, Mohd Taha and Khan, Arshad Hussain
- Abstract
AbstractThe large amplitude steady state periodic response of truncated conical shell panels under the influence of transverse harmonic excitation is analyzed by considering the nonlinear strain displacement relations. The finite element analysis is based on the kinematics of first-order shear deformation theory and the constrained strain terms have been interpolated using field-consistent modified shape functions to avoid shear locking. The governing equation of motion has been obtained using Hamilton’s principle, which has been solved using the Modified shooting method and continuation schemes to yield the complete frequency response. The influence of boundary conditions, the amplitude of the forcing function and curvature on the periodic response was investigated. The hardening or softening nonlinear behavior has been obtained depending upon boundary conditions, geometry and forcing function amplitude. The combined influence of geometric nonlinearity and varying curvature of the truncated conical shell leads to significantly greater negative half-cycle amplitude. The peculiar nature of the restoring force dynamics with increased inward deflection causes the restoring forces to act in a destabilizing sense leading to increase in negative half-cycle amplitude. The periodic stress variation reveals multiple stress reversals during a loading cycle and is very critical for the fatigue design of such components. The multiple slope changes/bifurcations in the frequency response have been examined using response history, frequency spectra and the phase plane plots where it is revealed that for some cases the higher harmonic contributions are even greater than the fundamental harmonic. The deformed configuration at various instants during the periodic cycle reveals modal interaction between first and higher modes. Moreover, the nonlinear frequency response curves depict softening nonlinear behavior for deeper shells which gradually transforms into hardening behavior for shallow shell panels. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Chains with Connections of Diffusion and Advective Types.
- Author
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Kashchenko, Sergey
- Subjects
- *
NONLINEAR boundary value problems , *QUASILINEARIZATION , *BOUNDARY value problems - Abstract
The local dynamics of a system of oscillators with a large number of elements and with diffusive- and advective-type couplings containing a large delay are studied. Critical cases in the problem of the stability of the zero equilibrium state are singled out, and it is shown that all of them have infinite dimensions. Applying special methods of infinite normalization, we construct quasinormal forms, namely, nonlinear boundary value problems of the parabolic type, whose nonlocal dynamics determine the behavior of the solutions of the initial system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of the dynamical properties of the original problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. INVERTEBRATES AND CATTLE POPULATION DYNAMICS IN A GRASSLAND ENVIRONMENT: A NONLINEAR INTER-SPECIFIC COMPETITION MODEL.
- Author
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TANDON, ABHINAV and DUTTA, VAISHNUDEBI
- Subjects
- *
INVERTEBRATE populations , *POPULATION dynamics , *COMPETITION (Biology) , *GRASSLANDS , *HOPF bifurcations , *DIFFERENTIAL equations , *BIOMASS - Abstract
In the proposed study, a nonlinear model is developed to explore the interactive dynamics between cattle and invertebrates when they coexist in a grassland system and compete with one another for the same resource — the grass biomass. The constructed model is theoretically investigated using the qualitative theory of differential equations to show the system's rich dynamical properties, which are crucial for maintaining the ecosystem's balance in grasslands. The qualitative findings show that, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. The model results support the idea that inter-specific competition between cattle and invertebrates does not always produce regular dynamic patterns but may also produce periodic and destabilizing patterns. The model's outputs may assist in striking a balance between pasture and natural grass biomass in grassland with the invertebrates. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Bifurcations, chaotic behavior, sensitivity analysis and soliton solutions of the extended Kadometsev–Petviashvili equation.
- Author
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Xu, Chongkun, ur Rahman, Mati, and Emadifar, Homan
- Subjects
- *
SENSITIVITY analysis , *KADOMTSEV-Petviashvili equation , *SYSTEMS theory , *RUNGE-Kutta formulas , *EQUATIONS , *QUANTUM chaos , *BIFURCATION diagrams - Abstract
The main aim of this study is to conduct an in-depth exploration of a recently introduced extended variant of the Kadomtsev–Petviashvili (KP) equation. To achieve this goal, we employ the Galilean transformation to derive the dynamic framework associated with the governing equation. Subsequently, we apply the principles of planar dynamical system theory to perform a bifurcation analysis. By incorporating a perturbed element into the established dynamic framework, we explore the potential emergence of chaotic behaviors within the extended KP equation. This investigation is supported by the presentation of phase portraits in both two and three dimensions. Additionally, to ascertain the stability of solutions, we conduct a sensitivity analysis on the dynamic framework employing the Runge–Kutta method. Our results affirm that minor variations in initial conditions have minimal impact on solution stability. Furthermore, employing the modified tanh method, we construct multiple instances of solitons and kinks for the proposed model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Numerical and Mathematical Modeling of a Gene Network with Nonlinear Degradation of the Components.
- Author
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Golubyatnikov, V. P., Kirillova, N. E., and Minushkina, L. S.
- Abstract
For a 3-dimensional dynamical system considered as a model of a gene network with nonlinear degradation of its components, the uniqueness of an equilibrium point is proved. Using approaches of qualitative theory of ordinary differential equations, we find conditions of existence of a cycle of this system and describe an invariant domain which contains all such cycles in the phase portrait. Numerical experiments with trajectories of this system are conducted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Weakly nonlinear analysis of thermoacoustic oscillations in can-annular combustors.
- Author
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Orchini, Alessandro and Moeck, Jonas P.
- Subjects
COMBUSTION chambers ,NONLINEAR analysis ,REDUCED-order models ,TRANSIENTS (Dynamics) ,NONLINEAR equations ,ACOUSTIC couplers ,NONLINEAR oscillators ,EIGENFREQUENCIES - Abstract
Can-annular combustors feature clusters of thermoacoustic eigenvalues, which originate from the weak acoustic coupling between N identical cans at the downstream end. When instabilities occur, one needs to consider the nonlinear interaction between all N modes in the unstable cluster in order to predict the steady-state behaviour. A nonlinear reduced-order model for the analysis of this phenomenon is developed, based on the balance equations for acoustic mass, momentum and energy. Its linearisation yields explicit expressions for the N complex-valued eigenfrequencies that form a cluster. To treat the nonlinear equations semianalytically, a Galerkin projection is performed, resulting in a nonlinear system of N coupled oscillators. Each oscillator represents the dynamics of a global mode that oscillates in the whole can-annular combustor. The analytical expressions of the equations reveal how the geometrical and thermofluid parameters affect the thermoacoustic response of the system. To gain further insights, the method of averaging is applied to obtain equations for the slow-time dynamics of the amplitude and phase of each mode. The averaged system, whose solutions compare very well with those of the full oscillator equations, is shown to be able to predict complex transient dynamics. A variety of dynamical states are identified in the steady-state oscillatory regime, including push-push (in-phase) and spinning oscillations. Notably, the averaged equations are able to predict the existence of synchronised states. These states occur when the frequencies of two (or more) unstable modes with nominally different frequencies lock onto a common frequency as a result of nonlinear interactions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Dynamical behavior and multiple optical solitons for the fractional Ginzburg–Landau equation with β-derivative in optical fibers.
- Author
-
Tang, Lu
- Subjects
- *
OPTICAL solitons , *DIFFERENTIABLE dynamical systems , *HAMILTON'S principle function , *SYMBOLIC computation , *BIFURCATION theory - Abstract
The main goal of the current work is to study dynamical behavior and dispersive optical solitons for the fractional Ginzburg–Landau equation in optical fibers. Starting with the traveling wave transformations, the fractional Ginzburg–Landau model is converted into an equivalent ordinary differential traveling wave system. Then, the Hamiltonian function and orbits phase portraits of this system are found. Here, we derived explicit fractional periodic wave solutions, bell-shaped solitary wave solutions and kink-shaped solitary wave solutions through the bifurcation theory of differential dynamical system. In addition to, some other traveling wave solutions are obtained by using the polynomial complete discriminant method and symbolic computation. Most notably, we give the classification of all single traveling wave solutions of fractional Ginzburg–Landau equation at the same time. The obtained optical soliton solutions in this work may substantially improve or complement the corresponding results in the known references. Finally, we give the comparison between our solutions and other's results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters.
- Author
-
Jorba-Cuscó, Marc, Oliva-Zúniga, Ruth I., Sardanyés, Josep, and Pérez-Palau, Daniel
- Subjects
- *
VECTOR fields , *ORBITS (Astronomy) , *POPULATION dynamics , *ENDANGERED species , *DYNAMICAL systems - Abstract
A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Dynamics of a plant-herbivore system with Ricker plant growth and the strong Allee effects on plant population.
- Author
-
Bešo, Emin, Kalabušić, Senada, and Pilav, Esmir
- Subjects
ALLEE effect ,PLANT populations ,PLANT growth ,SYSTEM dynamics ,COMPUTER simulation - Abstract
We examine a discrete-time model of plant-herbivore interaction, in which the population of plants follows the Ricker law and is affected by strong Allee effects. We discuss the equilibrium points, including their characteristics and number. Additionally, we analyze in detail the local behavior of the solutions around the equilibrium points. Under certain initial conditions, both populations may go extinct. We conduct research demonstrating the occurrence of transcritical and period-doubling bifurcations, resulting in a stable two-cycle at the boundary equilibrium. However, the interior equilibrium becomes unstable due to the emergence of the Neimark-Sacker bifurcation and period-doubling. We confirm the latter's existence through analytical methods and illustrate the period-doubling bifurcation through numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model.
- Author
-
Rizzi, Peter, Sander, Evelyn, and Wanner, Thomas
- Subjects
DIBLOCK copolymers ,PARABOLIC differential equations ,CYCLIC groups ,COPOLYMERS - Abstract
The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation points. Many of these bifurcations are of pitchfork type. In previous work, the authors showed that if pitchfork bifurcations are induced by a simple $ {\mathbb Z}_2 $ symmetry-breaking, then computer-assisted proof techniques can be used to rigorously validate them using extended systems. However, many diblock copolymer pitchfork bifurcations cannot be treated in this way. In the present paper, we show that in these more involved cases, a cyclic group action is responsible for their existence, based on cyclic groups of even order. We present theoretical results establishing such bifurcation points and show that they can be characterized as nondegenerate solutions of a suitable extended nonlinear system. Using the latter characterization, we also demonstrate that computer-assisted proof techniques can be used to validate such bifurcations. While the methods proposed in this paper are only applied to the diblock copolymer model, we expect that they will also apply to other parabolic partial differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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