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The studies on Nonlinear Phenomena have been carried out in buck converter controlled by three different types of modulation technique—Peak current, Peak V2 and Enhanced V2. These three modulation methods are rippled based control methods as inductor current ripple is used in Peak current modulation (PCM) method and output ripple voltage used in both Peak V2 and Enhanced V2 modulation methods and due to that all three modulation methods provide fast dynamic response. Here three modulation techniques have been explained in details and simulation results have been provided. For designing the modulators—we consider two loops i.e. inner loop or fast feedback path (FFBP) and outer loop or slow feedback path (SFBP). The outer loop of all these three modulation methods contains same information, the difference between reference voltage and output voltage. Mathematical model has been developed with the help of state space equation in continuous conduction mode (CCM). Bifurcation diagrams are obtained with load resistance, input voltage and reference voltage as bifurcation parameter. To validate the bifurcation pattern, time plot and phase plane trajectory at each transition have been shown for these three types of modulated system. A comparative study has been made. Experiments are conducted on an enhanced V2 modulated buck converter to validate the nature of the nonlinearities. To check the dependency of the system on ESR value, parameter space plots are developed and compared for all these three types of control technique. [ABSTRACT FROM AUTHOR]

In this paper, a quad-trophic food chain model with Beddington–DeAngelis functional response is formulated by incorporating fear effect and prey refuge. Firstly, it is proved that the system is dissipative. Five types of equilibria are identified, and the criteria for local and global stabilities of the coexistence equilibrium are deduced by Routh–Hurwitz criteria and Li–Muldowney geometric approach. Secondly, multiple bifurcations are explored. It is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation by the Sotomayor’s theorem, Hopf Bifurcation by normal form theory, heteroclinic bifurcation and homoclinic bifurcation by stability analysis of manifolds. Moreover, we present numerical experiments to verify the correctness of theoretical analysis. In particular, it is observed that the system undergoes period doubling and period halving cascades, cataclysm, and quasi periodic bifurcation (a torus), thereby entering or escaping chaotic state. It is also observed a saddle-focus homoclinic loop, a period two saddle-focus homoclinic loop, and a period three saddle-focus homoclinic loop for the system. Finally, it is found that fear effect and prey refuge can stabilize the system. [ABSTRACT FROM AUTHOR]

Introduction: The gear-bearing system plays a critical role in turbo-machinery. Nonlinear dynamics of the system, particularly the suspension effects, gear mesh forces, and temperature-dependent viscosity, significantly influence its performance. Understanding the system’s behavior, especially under varying rotational speeds and temperatures, is essential to avoid catastrophic failures. This study investigates the nonlinear dynamic behavior of a pinion/gear system under such conditions. Purpose: The purpose of this study is to systematically analyze the nonlinear dynamic behavior of a gear-bearing system, considering the effects of nonlinear suspension, nonlinear oil-film forces, nonlinear gear mesh forces, and temperature-dependent viscosity. The study aims to identify chaotic motions and other dynamic behaviors under various operational conditions. Methods: The nonlinear dynamic equations governing the system are solved using the fourth-order Runge–Kutta method, with a time step of π/300 and a convergence criterion of less than 0.0001. Several analytical tools, including bifurcation diagrams, dynamic trajectories, Poincaré maps, Lyapunov exponents, and fractal dimensions, are used to analyze the system’s behavior. The bifurcation control parameters include the dimensionless rotational speed ratio, unbalance parameter, and damping ratio, with a focus on different temperatures (T = 25 °C, 40 °C, 50 °C, and 80 °C). Results: The study finds a wide range of dynamic behaviors, including periodic, sub-harmonic, and chaotic motions. The bifurcation diagrams indicate transitions from irregular to regular motions at various rotational speeds, with non-periodic motions observed at higher speeds. The Poincaré maps and Lyapunov exponents confirm the onset of chaotic behavior, particularly at certain rotational speeds and temperatures. The dynamic responses of the gear and bearing geometric centers are often non-synchronous, with synchronization occurring at specific points. Temperature increases result in the degradation of lubrication and larger vibration amplitudes, especially at high speeds. Discussion: The findings highlight the importance of considering temperature-dependent viscosity in dynamic analyses. Neglecting temperature effects, particularly at low rotational speeds, can significantly underestimate the system’s dynamic behavior. The non-synchronous dynamic behavior of the bearing and gear centers under varying operational conditions emphasizes the need for careful selection of parameters such as damping ratio and unbalance to avoid chaotic motions. These results provide valuable insights into the design and optimization of gear-bearing systems, ensuring reliability and extending service life. [ABSTRACT FROM AUTHOR]

The isolated boost full-bridge converter (IBFBC) is a DC–DC conversion topology that achieves a high boost ratio and provides electrical isolation, making it suitable for applications requiring both. Its operational dynamics are often intricate due to its inherent characteristics and the prevalent usage of nonlinear switching elements, leading to bifurcation and chaos. Chaos theory was employed to investigate the impact of changes in the voltage feedback coefficient K and input voltage E on the dynamic behavior of the IBFBC when operating in discontinuous conduction mode (DCM). Based on an analysis of its operating principles, a discrete iterative mapping model of the system in DCM is constructed using the stroboscopic mapping method. The effects of two control parameters, namely the proportional coefficient and input voltage, on system performance are studied using bifurcation diagrams, fold diagrams, Poincaré sections, and Lyapunov exponents. Simulation experiments are conducted using time-domain and waveform diagrams to validate the discrete mapping model and confirm the correctness of the theoretical analysis. The results indicate that when the IBFBC operates in DCM, its operating state is influenced by the voltage feedback coefficient K and input voltage E . Under varying values of K and E , the system may operate in a single-period stable state, multi-period bifurcation, or chaotic state, exhibiting typical nonlinear behavior. [ABSTRACT FROM AUTHOR]

Nonlinear equations are essential in research and engineering because they simulate complicated processes such as fluid dynamics, chemical reactions, and population growth. The development of advanced methods to address them becomes essential for scientific and applied research enhancements, as their resolution influences innovations by aiding in the proper prediction or optimization of the system. In this research, we develop a novel biparametric family of inverse parallel techniques designed to improve stability and accelerate convergence in parallel iterative algorithm. Bifurcation and chaos theory were used to find the best parameter regions that increase the parallel method's effectiveness and stability. Our newly developed biparametric family of parallel techniques is more computationally efficient than current approaches, as evidenced by significant reductions in the number of iterations and basic operations each iterations step for solving nonlinear equations. Engineering applications examined with rough beginning data demonstrate high accuracy and superior convergence compared to existing classical parallel schemes. Analysis of global convergence further shows that the proposed methods outperform current methods in terms of error control, computational time, percentage convergence, number of basic operations per iteration, and computational order. These findings indicate broad usage potential in engineering and scientific computation. [ABSTRACT FROM AUTHOR]

A thermal tooth backlash model of a planetary gear system, which includes the effects of thermal deformation and thermal elastohydrodynamic lubrication film, was established. The variation laws of tooth backlash under variable speed, variable torque, and constant power conditions, as well as the nonlinear dynamic characteristics of the system were analyzed. The results showed that the change in tooth backlash is greatly influenced by thermal deformation numerically, while the thermal elastohydrodynamic lubrication film affects the trend of tooth backlash along the meshing line direction. Combining bifurcation diagrams, Largest Lyapunov exponent plots, poincaré sections, phase portraits, and frequency spectra analysis reveals that under variable speed and constant power conditions, the presence of thermal tooth backlash reduces the chaotic range of the system and transforms some unstable motion states into more stable ones. However, for variable torque conditions, the influence of thermal tooth backlash on the system is more complex with both stable and unstable situations coexisting. This study provides a theoretical basis for selecting backlash parameters in planetary gear system design and avoiding chaotic responses. [ABSTRACT FROM AUTHOR]

Purpose: To explore the impact of gear floating on the system's nonlinear dynamic characteristics, a gear floating model was developed based on the concept of gear floating. Methods: A nonlinear dynamic model, bending-torsional-axial-pendular (BTAP), has been developed for a coaxial reverse closed differential herringbone gear transmission system (CRCDHGTS), accounting for gear floating. This model considers factors such as gear floating backlash, tooth surface friction, gyroscopic effects, time-varying meshing stiffness (TVMS), meshing damping, and dynamic meshing parameters. A calculation model for the floating backlash and floating TVMS of a herringbone gear system was derived, and the nonlinear dynamic response of the gear system was solved using the Runge–Kutta method. Results: The influence of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams, including bifurcation diagrams, maximum Lyapunov exponent (MLE) plots, time history diagrams, frequency diagrams, phase diagrams, and Poincaré section diagrams. Conclusions: The research reveals that gear floating diminishes the chaotic motion behavior of the system under different excitation factors, thereby improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, rendering it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0–20 μm and 34–43 μm for generating periodic motion, with floating values around 10–20 μm demonstrating better performance in mitigating the negative effects of initial backlash and transmission error. [ABSTRACT FROM AUTHOR]

A control strategy combining cubic displacement feedback nonlinear control and proportional-differential (PD) linear control is used to control the vibration performance of the maglev system. The maglev system is divided into positive stiffness maglev system, quasi-zero stiffness maglev system and negative stiffness maglev system according to the linear stiffness value of maglev system. Firstly, an improved multi-scale method is used to analyze the vibration characteristics of suspension in the positive stiffness state of the maglev system. Secondly, the influence of control parameters on train vibration amplitude and vibration center displacement under quasi-zero stiffness is studied. Finally, the vibration characteristics of the train when the maglev system is in negative stiffness are analyzed by numerical simulation. The maglev system exhibits the worst vibration performance under negative stiffness compared with positive stiffness and quasi-zero stiffness. The suspension frame is easy to enter the chaotic motion state, and its vibration center is easy to deviate from the equilibrium position and produce large displacement when the maglev system is in the negative stiffness state. The control results show that the control strategy combining the cubic displacement feedback nonlinear control with the PD linear control can make the maglev system exhibit better vibration characteristics under positive and quasi-zero stiffness. [ABSTRACT FROM AUTHOR]

In a recent paper [Belykh et al., 2024], we proved that the bifurcation structure of a quadratic noninvertible map persists when the parameter increases from zero and the map turns into an invertible multidimensional Henon map. In this paper, we consider a similar problem for a generalized map which combines the Henon-type maps, the Poincaré return map for Shilnikov bifurcation of saddle-focus homoclinic orbit, the Lurie discrete time system, etc. We have obtained the expected result about the persistence of periodic orbits and their bifurcations when passing from a One-Dimensional (1D) endomorphism to the generalized map as a small parameter becomes nonzero. We have revealed the precise mechanism of change of homoclinic orbits and splitting of unstable manifolds as a result of the transition of 1D endomorphism to multidimensional map. Thereby we have derived the reconstruction rules of nonwandering set of orbits and bifurcations of the generalized map from those of 1D endomorphism. [ABSTRACT FROM AUTHOR]

In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W-shape, M-shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains. [ABSTRACT FROM AUTHOR]

With the widespread application of chaotic systems in many fields, research on chaotic systems is becoming increasingly in-depth. This article first proposes a new dynamic model of financial risk contagion based on financial principles and discusses some basic dynamic characteristics of the new chaotic system, such as equilibrium points, dissipativity, Poincaré diagrams, bifurcation diagrams, etc. Secondly, with the consideration of privacy during data transmission, the method was designed to protect the privacy of controlled systems in finite time based on perturbation. A controller designed for finite time was developed based on Lyapunov stability principles, which achieves system synchronization within a finite time and protects the privacy of the controlled system. The effectiveness was also verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper explores the dynamics of an eco-epidemiological prey-predator model, identifying four equilibria and analyzing their behaviors under various parameter settings. We investigate four bifurcations, Fold, Andronov-Hopf, Fold-Hopf, and Bogdanov-Takens, using central manifold and normal form calculations to assess their impact on system stability. We examine the system’s transitions between periodic and chaotic states by employing tools such as time series analysis, Lyapunov exponents, bifurcation diagrams, Poincare sections, and phase space reconstruction. We discover a self-excited attractor and highlight the system’s sensitivity to initial conditions and parameter changes. Additionally, we demonstrate the high accuracy of a Radial Basis Function Neural Network in modeling the system’s complex dynamics. This research advances our understanding of nonlinear dynamics and bifurcation theory in eco-epidemiological systems, offering valuable computational tools for future studies in ecological epidemiology and mathematical biology. [ABSTRACT FROM AUTHOR]

Abstract Magnetically coupled resonant wireless power transfer (MCR‐WPT) system with constant power load (CPL), finds extensive applications in military, industrial, and medical treatment. However, this system can easily exhibit complex non‐linear behaviors under certain parameter conditions due to the influences of constant power loads, switching devices, and feedback controllers. These behaviors limit the effectiveness of controllers and reduce the efficiency and stability of the system. It is necessary to study the non‐linear characteristics of the MCR‐WPT system with CPL. The stroboscopic discrete mapping of the MCR‐WPT system with CPL is established. Then the system's non‐linear dynamics are analyzed theoretically using a bifurcation diagram, the maximal Floquet multipliers, and the maximal Lyapunov exponent spectrum obtained from the proposed discrete mapping. The results show that the MCR‐WPT system with CPL will exhibit rich non‐linear dynamics with the variation of the power of CPL, such as cyclic fold bifurcation, Neimark–Scaker bifurcation, border collision bifurcations, chaos, etc. The excellent alignment of experimental and theoretical outcomes in corresponding states confirms the accuracy of the proposed discrete mapping and the nonlinear analysis of the system. The results of this study can provide a reference for selecting parameters for an actual MCR‐WPT system with CPL.

Introduction/purpose: Studying the dynamics of the mutual influence of supply and demand is relevant in connection with the financial losses that arise due to uncertainty in demand and forecast errors. The work aims to build a mathematical model of the dynamics of this interaction for the market of one product. Methods: The paper proposes a mathematical model of the states of the supply-demand system, within the framework of which the processes occurring in this system are considered from the perspective of the methodology of economic synergetics. The mathematical model of dynamics has the form of a system of two differential equations with quadratic nonlinearity. Results: The use of the proposed model to reproduce various dynamic states of market self-regulation processes made it possible to identify the hierarchy of transition from stable dynamic regimes to unstable ones with the appearance of corresponding bifurcations. The main attention was paid to studying the behavior of the system at the boundaries of the stability region. Conclusion: The existence of a saddle-node bifurcation of limit cycles has been revealed, which suggests the appearance of stable self-oscillations in the case of a "soft" cycle and unstable ones in the case of a "hard" cycle. When studying a bifurcation of codimension two - "double zero" - special dynamic structures were discovered, determined by the properties of global bifurcations. This type of behavior is characterized by self-oscillations with a low frequency, which gives rise to the so-called "ultra-long waves" of the economic state.

Magnetically coupled resonant wireless power transfer (MCR‐WPT) system with constant power load (CPL), finds extensive applications in military, industrial, and medical treatment. However, this system can easily exhibit complex non‐linear behaviors under certain parameter conditions due to the influences of constant power loads, switching devices, and feedback controllers. These behaviors limit the effectiveness of controllers and reduce the efficiency and stability of the system. It is necessary to study the non‐linear characteristics of the MCR‐WPT system with CPL. The stroboscopic discrete mapping of the MCR‐WPT system with CPL is established. Then the system's non‐linear dynamics are analyzed theoretically using a bifurcation diagram, the maximal Floquet multipliers, and the maximal Lyapunov exponent spectrum obtained from the proposed discrete mapping. The results show that the MCR‐WPT system with CPL will exhibit rich non‐linear dynamics with the variation of the power of CPL, such as cyclic fold bifurcation, Neimark–Scaker bifurcation, border collision bifurcations, chaos, etc. The excellent alignment of experimental and theoretical outcomes in corresponding states confirms the accuracy of the proposed discrete mapping and the nonlinear analysis of the system. The results of this study can provide a reference for selecting parameters for an actual MCR‐WPT system with CPL. [ABSTRACT FROM AUTHOR]

In this work, we study the Nanoparticles (NPs) impact on a phytoplankton–zooplankton interaction model with Ivlev-like and Holling type-II functional responses. We found that the growth rate of phytoplankton reduces due to NPs. In the non-spatial model, we investigated boundedness, stability, bifurcation and chaos. The stability criteria is determined using the Routh–Hurwitz criterion. Hopf bifurcation is demonstrated with parameter K, which represents the NPs carrying capacity while interacting with phytoplankton. The normal theory is used to examine the Hopf bifurcation direction and the stability of bifurcating periodic solutions. Moreover, the stability of non-hyperbolic equilibrium points have been determined using the Center Manifold theorem. Also, the parameter β, which represents the interaction rate between NPs and phytoplankton, exhibits chaotic behavior. Furthermore, we also investigated Hopf bifurcation and Turing instability in spatial model systems. This study demonstrates that NPs can influence the dynamics of the system in a balanced environment. [ABSTRACT FROM AUTHOR]

In this work, we first discuss the positive equilibrium point of the continuous predator–prey system and its stability, and we discuss the parameter conditions under which the continuous system undergoes a cusp bifurcation (Bogdanov–Takens bifurcation) of codimension two bifurcation at the positive equilibrium point. Then, we provide an insightful study of discrete predator–prey systems by the use of Euler's method, which includes square-root function responses and nonlinear prey harvesting. By synthesizing the new standard form of differential-algebraic systems, the central manifold theorem, and the bifurcation theory, we identify the specific conditions under which the system may undergo flip bifurcation and Neimark–Sacker bifurcation. In addition, codimension-two bifurcations associated with 1:2 strong resonances are analyzed by using a series of affine transformations and bifurcation theory. Through numerical simulations, we not only verify the validity and correctness of our findings, but also elucidate the frequency of trajectory bifurcations in the intervals of 2, 4, and 8 and chaotic phenomena. These findings reveal a richer and more diverse dynamic behavior of discrete differential-algebraic bioeconomic systems, which is of great theoretical and practical significance to the fields of mathematics and biology. [ABSTRACT FROM AUTHOR]

This paper addresses the challenging issues of transmission quality degradation and difficulty in obtaining dynamic response characteristics caused by the nonlinear behavior of non-circular planetary gear systems (NPG). A dynamic model for NPG was developed, encompassing axial elastic displacement, backlash, tooth surface friction, time-varying meshing stiffness, and viscoelastic damping. Fourier fitting matrices for time-varying mesh stiffness and polynomial models for dynamic backlash in non-circular gears were acquired to enhance model precision. Various analysis techniques including phase trajectory diagrams, bifurcation diagrams, time history diagrams, Poincaré mapping diagrams, and phase amplitude frequency characteristic curves were used to evaluate the nonlinear behavior of NPGs. Research results indicate that increasing the damping ratio benefits frequency response bandwidth, reduces phase lag, and improves system stability. The friction coefficient on the surface of non-circular gears also plays a role in ensuring the stability and phase consistency of NGP, although excessive coefficients can induce chaos. The output solar gear is more sensitive to internal excitation, with higher internal excitation leading to stronger system chaos. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model. [ABSTRACT FROM AUTHOR]

The classical Hastings–Powell model is well known to exhibit chaotic dynamics in a three-species food chain. Chaotic dynamics appear through period-doubling bifurcation of stable coexistence limit cycle around an unstable coexisting equilibrium point. A specific choice of parameter value leads to a situation, where the chaotic attractor disappears through a collision with an unstable limit cycle originated due to subcritical Hopf-bifurcation around the coexistence equilibrium. As a consequence, the top predator goes to extinction. The main objective of this work is to explore the structural sensitivity of this phenomenon by replacing the Holling-type II functional responses with Ivlev functional responses. In this work, we have shown the existence of two Hopf-bifurcation thresholds and numerically verified the existence of an unstable limit cycle. The model with Ivlev functional responses does not indicate any possibility of extinction of the top predator due to any collision of chaotic attractor with the unstable limit cycle for the chosen range of parameter values. Moreover, the model with Ivlev functional responses depicts an interesting scenario of bistable oscillatory coexistence. [ABSTRACT FROM AUTHOR]

Copyright of Military Technical Courier / Vojnotehnicki Glasnik is the property of Military Technical Courier / Vojnotehnicki Glasnik and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We studied the nonlinear dynamics of a shunted inductive Josephson junction coupled to a diode and a negative conductance. Taking into account the non-harmonicity of the junction, based on Kirchhoff's laws, we have developed the mathematical model which governs the dynamics of the circuit. The fixed points of the system are determined, and their stabilities are analyzed using the Routh–Hurwitz criterion. The bifurcation and transition to chaos of the model are studied using the the fourth-order Runge–Kutta method; the system displays a rich dynamics. The range of values of each parameter leading to periodic and chaotic electrical oscillations is obtained through the analysis of the effect of these parameters on each type of dynamics. Finally, the implementation by microcontroller is carried out in order to experimentally verify the different dynamics obtained numerically. [ABSTRACT FROM AUTHOR]

Medical images make up for more than 25% of global attacks on privacy. Securing them is therefore of utmost importance. Chaos based image encryption is one of the most method suggested in the literature for image security due to their intrinsic characteristic, including ergodicity, aperiodicity, high sensitivity to initials conditions and system parameters. Dynamic systems such as bridge circuit, jerk circuit, Van der Pol circuit, Colpitts oscillator and many other pseudo-random numbers generators have been used in the process of encrypting images. Among them, are the jerk oscillators that have been used with different nonlinearities. In this paper, a new, simple, off-shell component of jerk oscillator (jerk quintic) with an interesting nonlinear function is proposed. Its dynamical behaviors are investigated using classical tools like bifurcation diagrams, Maximum Lyapunov exponent plot, basin of attraction, phase portraits. We showed that the nonlinear function is responsible of complex nonlinear behaviors displayed by the novel circuit, including symmetric/asymmetric bifurcation and coexisting bubbles, multistability just to name a few. The real implementation of the interesting circuit is embedded in a microcontroller verifies these dynamics. As an application of this contribution in multimedia, an encryption algorithm built on a new confusion-diffusion architecture using pseudo random number generated in high chaoticity regime of the new circuit is proposed. The cryptosystem underwent thorough security tests and proved to be fast thanks to the 3D map used, given its complex dynamical behaviors and large chaotic area. This approach yields a robust cipher that underwent thorough security tests better than the one in the literature like average NPCR=99.61, UACI=33.48, key space-sensitivity, entropy=7.9994, average correlation=0.0040. Furthermore, it proved to be robust in terms of noise and data loss in the transmission channel, offering a large key space of 10180 and an entropy close to the standard value, thus rendering the cryptosystem robust against various attacks, especially brute force and exhaustive attacks. [ABSTRACT FROM AUTHOR]

We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model's ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research. [ABSTRACT FROM AUTHOR]

Abstract This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

Abstract This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

This study seeks to explore the integrable dynamics of induced curves through the utilization of the complex-coupled Kuralay system. The importance of the coupled complex Kuralay equation lies in its role as a fundamental model that contributes to the understanding of intricate physical and mathematical concepts, making it a valuable tool in scientific research and applications. The soliton solutions originating from the Kuralay equations are believed to encapsulate cutting-edge research in various important domains such as optical fibers, nonlinear optics, and ferromagnetic materials. Analytical techniques are employed to derive traveling wave solutions for this model, given that the Cauchy problem cannot be resolved using the inverse scattering transform. In the quest for solitary wave solutions, the extended modified auxiliary equation mapping (EMAEM) method is employed. We derive several novel families of precise traveling wave solutions, encompassing trigonometric, hyperbolic, and exponential forms. Moreover, the planar dynamical system of the concerned equation is created, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are incorporated alongside the analytical results to enhance comprehension of the dynamic characteristics of the solutions obtained. This study’s outcomes can offer valuable insights for addressing other nonlinear partial differential equations (NLPDEs). The soliton solutions obtained in this study offer important insights into the intricate nonlinear equation being examined. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis. • A new formulation on semi-analytical time-domain model for fluidelastic instability of tube bundles. • The formulation has explicit fluid force expressions. • Linear frequency- and time-domain analysis are validated against available experimental and theoretical results. • Nonlinear dynamics behavior of a loosely-supported tube is probed based on the new formulation by using various techniques. • The route to chaos of the system is found through quasi-periodic to chaos. [ABSTRACT FROM AUTHOR]

This research investigates the interaction between a generalist predator and a prey, where the predator exhibits cooperative behavior during hunting, inducing fear into the prey population. Additionally, both the prey and predator populations are subject to harvesting. The study establishes the positivity and boundedness of the model's solutions, ensuring the existence of the population. Analyzing the system, we explore its feasible steady states and their stability, along with various types of bifurcations, including Hopf with direction of stability, Saddle-node, Transcritical, Homoclinic, Bogdanov–Takens, and Cusp bifurcation. We also demonstrate the stability and bifurcation behavior of a delayed system. These findings are verified through one-parameter and two-parameter bifurcation structures, complemented by respective phase portraits. Notably, the system displays transition between different equilibria and bistability. Furthermore, numerical investigations reveal the impact of gestation delay, indicating chaotic behavior in the system due to this time delay. [ABSTRACT FROM AUTHOR]

This paper conducts an in-depth study on the dynamic stability and complex vibration behavior of a 12-pole active magnetic bearing (AMB) system considering gravitational effects under a PD controller. Firstly, based on electromagnetic theory and Newton's second law, a two-degree-of-freedom control equation of the system, including PD control terms and gravitational effects, is constructed. This equation involves not only parametric excitation, quadratic nonlinearity, and cubic nonlinearity but also a more pronounced coupling effect between the magnetic poles due to the presence of gravity. Secondly, using the multi-scale method, a four-dimensional averaged equation of the system in Cartesian and polar coordinates is derived. Finally, through numerical analysis, the system's amplitude–frequency response, motion trajectory, the relationship between energy and amplitude, and global dynamic behaviors such as bifurcation and chaos are discussed in detail. The results show that the PD controller significantly affects the system's spring hardening/softening characteristics, excitation, amplitude, energy, and stability. Specifically, increasing the proportional gain can quickly suppress the rotor's motion, but it also increases the system's instability. Adjusting the differential gain can transition the system from a chaotic state to a stable periodic motion. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The carrying capacity's functional dependence illustrates the reality that any species' activities can enhance or diminish its carrying capacity. Migration is the need of many species to achieve better opportunities for survival. In a tri-trophic system, the middle predator often immigrates to consume its prey and often emigrates to secure themselves from predators. This work deals with formulating and investigating a mathematical model reflecting the aforementioned ecological aspects. We perform a detailed analysis to prove the boundedness of the solutions. Further, we examine the existence and stability of equilibrium points, followed by the bifurcation analysis. We explore various global and local bifurcations like Hopf, saddle-node, transcritical, and homoclinic for the critical parameters β (measuring the impact of prey activities on the carrying capacity) and k 1 (measuring the migration rate of a predator). Higher values of β generate unpredictability, which helps explain the enrichment paradox. The presence of a chaotic attractor and bi-stability of node-node type is demonstrated via numerical simulation. The migratory behavior of middle predators can control chaos in the system. Furthermore, we study the proposed model in the presence of seasonal fluctuations. Persistence of the non-autonomous system, existence, and global stability of periodic solutions are analyzed theoretically. The seasonality in β brings the bi-stability between chaotic and periodic attractors, and seasonality in growth rate of the prey causes bi-stability between 2-periodic and 4-periodic attractors. Moreover, the bi-stability in the autonomous system shifts to the global stability of an equilibrium in the seasonal model due to the seasonality in β . When birth and death rates are seasonal along with β , the extinction of one or more populations is possible. The non-autonomous system also exhibits bursting oscillations when seasonality is present in the death rate. Our findings reveal that the population's intense constructive and destructive actions can allow the basal prey to thrive while eradicating both predators. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the dynamics of a fourth-order Newtonian iterative method for finding roots of polynomials of degrees three and four. Unlike traditional fourth-order methods requiring third derivatives, this technique avoids them by using the same derivative order in each of its three steps per iteration. When applied to differentiable functions, the method generates chaotic dynamics, as shown for quartic polynomials. Specifically, we apply this root-finding approach to the bifurcation diagram of the logistic map over an interval. Our findings demonstrate the potential for complex behavior even in simple iterative methods, and highlight the usefulness of this approach for exploring polynomial system dynamics. The paper identifies examples of fourth-degree polynomials, explains bifurcation, and chaos. [ABSTRACT FROM AUTHOR]

Memristor synapses have been widely introduced into neuronal models to investigate the effects of external magnetic fields. However, there is a relative lack of research on the external-induced electric fields in neurons. In this paper, a 4D-memristive Hindmarsh–Rose neuron model is constructed by introducing a memristor and an electric field variable, which can generate complex neural firing. Notably, numerical simulations reveal that the initial conditions of the memristor can induce different firing patterns, exhibiting a unique fractal structure in the basin of attractions. Remarkably, the offset parameters of the internal variables of the neuron can be canceled out so that the offset boosting of the variables can be achieved according to the initial values, giving rise to an uncountably many hidden attractors with homogeneous multistability. This model provides the first example of generating uncountably many attractors in a memristive neuron model without relying on trigonometric functions, significantly advancing our understanding of neuronal dynamics. Finally, a digital circuit is designed and implemented on the RISC-V platform to verify the numerical simulation and theoretical analysis. The findings of this study have a certain implication for the development of advanced neuromorphic computing systems and the understanding of complex neuronal behaviors in the presence of external electric fields. [ABSTRACT FROM AUTHOR]

A loan benchmark interest rate policy always becomes a challenging problem in the banking industry since it has a role in controlling bank loan expansion, especially when there is competition between two banks. This paper aims to assess the influence of the loan benchmark interest rate on the expansion of loans between two banks. We present a banking duopoly model in the form of two-dimensional difference equations which is constructed from heterogeneous expectation, where one of the banks sets its optimal loan volume based on the other bank’s rational expectation. The model‘s equilibrium is investigated, and its stability is analyzed using the Jury stability condition. Investigation indicates that to ensure the stability of the banking loan equilibrium, it is advisable to establish a loan benchmark interest rate that is lower than the flip bifurcation value. Some numerical simulations, such as the bifurcation diagram, Lyapunov exponent, and chaotic attractor, are presented to confirm the analytical findings. [ABSTRACT FROM AUTHOR]