4,692 results
Search Results
202. Transmission dynamics of discrete SEIR model.
- Author
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Adil, Riyam Ammar and Lafta, Alaa Hussein
- Subjects
- *
INFECTIOUS disease transmission , *HOPF bifurcations , *PHASE coding , *COMPUTER simulation , *EPIDEMICS - Abstract
This paper discussed the transmission dynamics of discrete SEIR model. It is possible to determine the prerequisites for the endemic and disease-free equilibria, as well as their local stability. In addition to demonstrating the validity of our findings, the numerical simulations also display more sophisticated dynamical characteristics such as the chaos phenomena, flip bifurcation, and Hopf bifurcation. These findings demonstrate that, as compared to models for both continuous and discrete epidemics exhibits far richer dynamical features. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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203. The Dynamics of Pasture–Herbivores–Carnivores with Sigmoidal Density Dependent Harvesting
- Author
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Bergland, Harald, Burlakov, Evgenii, and Wyller, John
- Published
- 2023
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204. An Analytic Investigation of Hopf Bifurcation Location Control for the Rulkov Map Model.
- Author
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Salehi Yekta, M., Zamani Bahabadi, A., and Sadeghi Bajestani, G.
- Subjects
- *
HOPF bifurcations , *NONLINEAR dynamical systems , *EPILEPSY , *NEUROLOGICAL disorders - Abstract
From the point of view of nonlinear dynamical systems, some neurological disorders can be indicated by bifurcations because bifurcations change the firing patterns of neurons; therefore, it is essential to control the bifurcations. We can avoid undesirable dynamical behaviors such as the behaviors of the Rulkov map model by controlling bifurcation which, then, can assist in modeling neuronal diseases. In this paper, we investigate the existence of Hopf bifurcation and analytically identify the type of bifurcation for the Rulkov map model; then, we apply a dynamic feedback controller using a washout filter to control the onset of Hopf bifurcation. Also, we can control the behaviors of the neurons, such as spiking or spiking-bursting behavior of neurons, and create the Hopf bifurcation for some parameters. The results analytically obtained in this paper can be applied to control some epileptic seizures. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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205. Similarity Transforming Techniques of Partial Differential Equations and its Applications: A review.
- Author
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Rashed, A. S. and Kassem, M. M.
- Subjects
- *
PARTIAL differential equations , *ORDINARY differential equations , *INDEPENDENT variables , *HOPF bifurcations , *SIMILARITY transformations - Abstract
The current paper is a review of some transformation techniques of partial differential equations (PDEs) using similarity techniques which have the ability to reduce the number of independent variables to be a single variable resulting in a simpler ordinary differential equation (ODEs). These techniques have the benefit to obtain some completely new solutions. The paper introduces a summary and literature review for method of characteristic lines, Bäcklund transformations, Cole-Hopf Transformation, Lie infinitesimals, Non-classical symmetry method, Potential Symmetry, direct methods and characteristic function method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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206. Phenomenology of an In-host Model of Hepatitis C.
- Author
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Nangue, Alexis and Rendall, Alan D.
- Abstract
This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive orthant is exhibited. It is proved that the model exhibits Hopf bifurcations and hence periodic solutions. A general parametrization of positive steady states is given and it is determined when the number of steady states is odd or even, according to the value of a certain basic reproductive ratio. This implies, in particular, that when this reproductive ratio is greater than one there always exists at least one positive steady state. A positive steady state which bifurcates from an infection-free state when the reproductive ratio passes through one is always stable, i.e. no backward bifurcation occurs in this model. The results obtained are compared with those known for related models of viral infections. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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207. MATHEMATICAL MODELING OF INFECTION MECHANISM BETWEEN MILD AND SEVERE COVID-19 PATIENTS.
- Author
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LAN, QING, WU, HUI, LOU, JIE, and LI, JIANQUAN
- Subjects
COVID-19 ,MATHEMATICAL models ,HOPF bifurcations ,T cells ,LEAST squares - Abstract
The SARS-CoV-2 leads to a worldwide COVID-19 pandemic, which has caused tremendous damage to the world. In this paper, we develop a dynamic model in vivo, fitting and estimating parameters for T lymphocytes and pro-inflammatory cytokines IL-6 in patients with mild and severe COVID-19 at Yale New Haven Hospital through the GWMCMC algorithm. Meanwhile, we also analyze the structural identifiability and practical identifiability of the model. Further, we add time-varying parameters to the model, using the least squares method to perform data fitting and parameter estimation on survivors and non-survivors of the Italian infectious disease hospital. Then analyze the similarities and differences in immune response mechanisms between the two countries. Finally, we demonstrate the existence and stability of the equilibrium state of the model and analyze the Hopf bifurcation at the positive equilibrium state by using the central manifold theory and normal form theory. This result may explain the recurrence of infection in some COVID-19 patients. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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208. BIFURCATION CONTROL STRATEGY FOR A DELAYED FRACTIONAL-ORDER POPULATION DYNAMICS MODEL WITH INCOMMENSURATE ORDERS.
- Author
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QI, HAO and ZHAO, WENCAI
- Subjects
HOPF bifurcations ,FRACTIONAL differential equations ,STABILITY theory - Abstract
This paper excogitates a bifurcation control strategy for a delayed fractional-order population dynamics model with incommensurate orders. First and foremost, by using stability theory of fractional differential equations, the sufficient conditions for the stability of the positive equilibrium are established. It is not difficult to find that the fractional-order system has a wider stability region than the traditional integer-order system. Second, taking time delay as bifurcation parameter, the sufficient criteria for Hopf bifurcation are obtained. In the next place, it is interesting to introduce a delayed feedback controller to guide Hopf bifurcation. The results reveal that the bifurcation dynamics of the model could be effectively controlled as long as the delay or fractional order is carefully adjusted. In conclusion, numerical simulations are carried out to confirm our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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209. DYNAMICAL BEHAVIORS OF A CLASS OF STOCHASTIC TUMOR–IMMUNE SYSTEMS.
- Author
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WANG, ZHEN and JIN, MENGMENG
- Subjects
STOCHASTIC systems ,STOCHASTIC analysis ,INVARIANT measures ,HOPF bifurcations - Abstract
In this paper, we consider a class of tumor–immune systems perturbed by the environmental noise and focus on the longtime behaviors. The existence and uniqueness of the globally positive solution to the tumor–immune system are proved using stochastic Lyapunov analysis and Itô's formula. We study the boundedness of moments for tumor cells and effector cells. By considering the dynamics on the boundary, applying the comparison theorem and the strong ergodic theorem, we obtain a threshold λ which is used to characterize the stochastic permanence in the sense that there is a unique invariant measure and extinction of the stochastic tumor–immune system. We also give biological interpretations about our analytical results of stochastic system. In addition, we present numerical examples and discussions to illustrate our analysis results. We find that the small noises preserve Hopf bifurcation of the deterministic system in stochastic setting and study numerically how the stochastic Hopf bifurcation with parameters occurs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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210. BIFURCATION ANALYSIS IN A TUMOR-IMMUNE SYSTEM INTERACTION MODEL WITH DENDRITIC CELL THERAPY AND IMMUNE RESPONSE DELAY.
- Author
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YUYUE ZHANG, LIQI XIE, YUEPING DONG, JICAI HUANG, SHIGUI RUAN, and YASUHIRO TAKEUCHI
- Subjects
CELLULAR therapy ,IMMUNE response ,HOPF bifurcations ,T cells ,DENDRITIC cells ,ACTIVATION energy ,HOPFIELD networks - Abstract
In this paper, we study a tumor-immune system interaction model with dendritic cell therapy and immune response delay. First, it is shown that the ODE version of the model has a Bogdanov--Takens (BT) singularity or a weak focus with multiplicity at most 1 for different parameter values. As the parameters vary, the ODE model undergoes supercritical Hopf bifurcation and supercritical BT bifurcation. Our analysis indicates that there exists a threshold value of the activation rate of T cells, below which tumor immune escape occurs, above or at which T cells and tumor cells coexist in the form of a stable periodic oscillation or steady state. Second, we study how the immune response delay affects the dynamics of the model. Our results reveal that the delay can destabilize the stable positive equilibrium through Hopf bifurcation. Furthermore, the direction and stability of Hopf bifurcation are derived. When there is a cusp, we show that it is a BT singularity for any delay and the delay model also undergoes BT bifurcation. Finally, numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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211. Hopf Bifurcation in a Reaction–Diffusion–Advection Two Species Model with Nonlocal Delay Effect.
- Author
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Li, Zhenzhen, Dai, Binxiang, and Han, Renji
- Subjects
HOPF bifurcations ,SPECIES - Abstract
The dynamics of a general reaction–diffusion–advection two species model with nonlocal delay effect and Dirichlet boundary condition is investigated in this paper. The existence and stability of the positive spatially nonhomogeneous steady state solution are studied. Then by regarding the time delay τ as the bifurcation parameter, we show that Hopf bifurcation occurs near the steady state solution at the critical values τ n (n = 0 , 1 , 2 , ...) . Moreover, the Hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold. The general results are applied to a Lotka–Volterra competition–diffusion–advection model with nonlocal delay. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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212. Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control.
- Author
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Miao, Pengcheng, Li, Denghui, Yue, Yuan, and Grebogi, Celso
- Subjects
MOTOR vehicle dynamics ,HOPF bifurcations ,CENTER of mass ,AUTOMOBILE steering gear - Abstract
In this paper, the stability and Bautin bifurcation of a four-wheel-steering (4WS) vehicle system, by considering driver steering control, are investigated. By using the central manifold theory and projection method, the first and second Lyapunov coefficients are calculated to predict the type of Hopf bifurcation of the vehicle system. The topological structure of Bautin bifurcation, a degenerate Hopf bifurcation of the 4WS vehicle system, is presented in parameter space, and it reveals the dynamics of the vehicle system of different choices of control parameters. The influences of system parameters on critical values of the bifurcation parameter are also analyzed. It is shown that with the increase in the frontal visibility distance of the driver control strategy coefficient and the cornering stiffness coefficients of rear wheels, the critical speed increases. Nevertheless, the critical speed decreases with the increase in the distance from the center of gravity of the vehicle to the front axles, Driver's perceptual time delay, and cornering stiffness coefficients of the front wheels. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
213. Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure.
- Author
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Li, Shuai, Huang, Chengdai, and Song, Xinyu
- Subjects
FUNCTIONAL equations ,HOPF bifurcations ,NEURONS - Abstract
In this paper, we formulate and study a fractional-order network model with four neurons, bidirectional ring structure and self-delay feedback. For the scenario of non-identical neurons, we develop a new algebraic technique to deal with the characteristic equation with e − 4 s τ (τ is the self-feedback delay) term and thus establish the easy-to-check criteria to determine the Hopf bifurcation point of self-feedback delay by fixing communication delay in its stable interval. For the scenario of identical neurons, we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation curve. The obtained results accommodate the fact that the model cannot preserve its stability behavior when the self-feedback delay crosses the Hopf bifurcation point in the positive direction. Finally, we deliberate on the correctness of our methodology through two demonstration examples. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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214. A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model.
- Author
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Ducrot, Arnaud, Kang, Hao, and Magal, Pierre
- Subjects
POPULATION dynamics ,IMPLICIT functions ,BIRTH rate ,HOPF bifurcations ,LOTKA-Volterra equations - Abstract
In this paper, we provide a short proof for the Hopf bifurcation theorem in the Gurtin-MacCamy's population dynamics model. Here we use the Crandall and Rabinowitz's approach, based on the implicit function theorem. Compared with previous methods, here we require the age-specific birth rate to be slightly smoother (roughly of bounded variation), but we have a huge gain for the length of the proof. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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215. Dynamics of a Discrete Leslie–Gower Model with Harvesting and Holling-II Functional Response.
- Author
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Zhang, Chen and Li, Xianyi
- Subjects
HARVESTING ,HOPF bifurcations ,ORBITS (Astronomy) ,COMPUTER simulation - Abstract
Recently, Christian Cortés García proposed and studied a continuous modified Leslie–Gower model with harvesting and alternative food for predator and Holling-II functional response, and proved that the model undergoes transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation. In this paper, we dedicate ourselves to investigating the bifurcation problems of the discrete version of the model by using the Center Manifold Theorem and bifurcation theory, and obtain sufficient conditions for the occurrences of the transcritical bifurcation and Neimark–Sacker bifurcation, and the stability of the closed orbits bifurcated. Our numerical simulations not only illustrate corresponding theoretical results, but also reveal new dynamic chaos occurring, which is an essential difference between the continuous system and its corresponding discrete version. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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216. Stability Analysis of a Mathematical Model for Adolescent Idiopathic Scoliosis from the Perspective of Physical and Health Integration.
- Author
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Zhang, Yuhua and Li, Haiyin
- Subjects
ADOLESCENT idiopathic scoliosis ,MATHEMATICAL analysis ,MATHEMATICAL models ,HOPF bifurcations - Abstract
In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a positive equilibrium under the delays of τ = 0 and τ ≠ 0 . Furthermore, through numerical simulation, it has been verified the delay, τ , exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
217. Dynamics of a three-molecule autocatalytic Schnakenberg model with cross-diffusion: Turing patterns of spatially homogeneous Hopf bifurcating periodic solutions.
- Author
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Li, Weiyu and Wang, Hongyan
- Subjects
HOPF bifurcations ,AUTOCATALYSIS ,DIFFUSION ,ORDINARY differential equations ,DYNAMICAL systems - Abstract
In this paper, a three-molecule autocatalytic Schnakenberg model with cross-diffusion is established, the instability of bifurcating periodic solutions caused by diffusion is studied, that is, diffusion can destabilize the stable periodic solutions of the ordinary differential equation (ODE) system. First, utilizing the local Hopf bifurcation theory, the central manifold theory, the normal form method and the regular perturbation theory of the infinite dimensional dynamical system, the stability of periodic solutions for the ODE system is discussed. Second, for this model, according to the implicit function existence theorem and Floquet theory, the Turing instability of spatially homogeneous Hopf bifurcating periodic solutions is studied. It is proved that the otherwise stable Hopf bifurcating periodic solutions in the ODE system produces Turing instability in the Schnakenberg model with cross-diffusion. Finally, through numerical simulations, it is verified that Turing instability of periodic solutions is determined by cross-diffusion rates. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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218. Stability and bifurcation of a delayed prey-predator eco-epidemiological model with the impact of media.
- Author
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Meng, Xin-You and Lu, Miao-Miao
- Subjects
PREDATION ,HOPF bifurcations ,STABILITY criterion ,HOPFIELD networks ,COMPUTER simulation - Abstract
In this paper, a delayed prey-predator eco-epidemiological model with the nonlinear media is considered. First, the positivity and boundedness of solutions are given. Then, the basic reproductive number is showed, and the local stability of the trivial equilibrium and the disease-free equilibrium are discussed. Next, by taking the infection delay as a parameter, the conditions of the stability switches are given due to stability switching criteria, which concludes that the delay can generate instability and oscillation of the population through Hopf bifurcation. Further, by using normal form theory and center manifold theory, some explicit expressions determining direction of Hopf bifurcation and stability of periodic solutions are obtained. What's more, the correctness of the theoretical analysis is verified by numerical simulation, and the biological explanations are also given. Last, the main conclusions are included in the end. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
219. Complicate dynamical analysis of a discrete predator-prey model with a prey refuge.
- Author
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Khan, A. Q. and Alsulami, Ibraheem M.
- Subjects
STATE feedback (Feedback control systems) ,HOPF bifurcations ,BIFURCATION theory ,LOTKA-Volterra equations ,PREDATORY animals - Abstract
In this paper, some complicated dynamic characteristics are formulated for a discrete predator-prey model with a prey refuge. After studying the local dynamical properties about fixed points, our main purpose is to investigate condition(s) for the occurrence of flip and hopf bifurcations, respectively. Further, by the bifurcation theory, we have studied flip bifurcation at boundary fixed point, and flip and hopf bifurcations at interior fixed point of the discrete model. We have also studied chaos by state feedback control strategy. Furthermore, theoretical results are numerically verified. Finally, we have also discussed the influence of prey refuge in the discrete model. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
220. Bifurcation and stability of a diffusive predator–prey model with the fear effect and time delay.
- Author
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Wang, Huatao, Zhang, Yan, and Ma, Li
- Subjects
HOPF bifurcations ,LYAPUNOV-Schmidt equation ,BIFURCATION theory ,PREDATION ,POPULATION density ,EIGENVALUES - Abstract
The predator–prey system can induce wealth properties with fear effects. In this paper, we propose a diffusive predator–prey model where the influence of fear effects and time delay is considered, under the Dirichlet boundary condition. It follows from the Lyapunov–Schmidt reduction method that there exists a non-homogeneous steady-state solution of the system and the specific expressions are also given. By the aid of bifurcation theory and eigenvalue theory, we also investigate the existence/non-existence and the stability of Hopf bifurcation under three different conditions of bifurcation parameters. Furthermore, the effects of the fear on population density, stability, and Hopf bifurcation are also considered and the results show that the increase of fear effects will reduce the population density, and Hopf bifurcation is more likely difficult to undergo as k increases under some conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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221. Tanh-like models for analysis and prediction of time-dependent flow around a circular cylinder at low Reynolds numbers.
- Author
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Wang, Libao, Xu, Min, Zheng, Boda, and An, Xiaomin
- Subjects
REYNOLDS number ,FLUID flow ,VORTEX shedding ,PREDICTION models ,HOPF bifurcations ,COORDINATE transformations - Abstract
When employing traditional low-order approximation equations to forecast the Hopf bifurcation phenomenon in the wake of a circular cylinder at low Reynolds numbers, inaccuracies may arise in estimating the phase. This is due to the fact that, in this transition process, the frequency varies with time. In this paper, we propose a method for analyzing and predicting the vortex shedding behind a cylinder at low Reynolds numbers. The proposed method is based on coordinate transformation and description function and is demonstrated using data from computational fluid dynamics simulation of flow around a cylinder at Reynolds number 100. The resulting governing equations explicitly contain the flow amplitude and implicitly contain the flow frequency. The proposed method is found to have higher accuracy compared to other methods for nonlinear identification and order reduction. Finally, the method is extended to predict nonlinear vortex shedding in the Reynolds number range of 80–200. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
222. Canard-induced mixed mode oscillations as a mechanism for the Bonhoeffer-van der Pol circuit under parametric perturbation.
- Author
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Yu, Yue, Zhang, Cong, Chen, Zhenyu, and Zhang, Zhengdi
- Subjects
OSCILLATIONS ,HOPF bifurcations ,BIFURCATION theory ,BIFURCATION diagrams ,PERTURBATION theory ,DIFFERENTIAL equations - Abstract
Purpose: This paper aims to investigate the singular Hopf bifurcation and mixed mode oscillations (MMOs) in the perturbed Bonhoeffer-van der Pol (BVP) circuit. There is a singular periodic orbit constructed by the switching between the stable focus and large amplitude relaxation cycles. Using a generalized fast/slow analysis, the authors show the generation mechanism of two distinct kinds of MMOs. Design/methodology/approach: The parametric modulation can be used to generate complicated dynamics. The BVP circuit is constructed as an example for second-order differential equation with periodic perturbation. Then the authors draw the bifurcation parameter diagram in terms of a containing two attractive regions, i.e. the stable relaxation cycle and the stable focus. The transition mechanism and characteristic features are investigated intensively by one-fast/two-slow analysis combined with bifurcation theory. Findings: Periodic perturbation can suppress nonlinear circuit dynamic to a singular periodic orbit. The combination of these small oscillations with the large amplitude oscillations that occur due to canard cycles yields such MMOs. The results connect the theory of the singular Hopf bifurcation enabling easier calculations of where the oscillations occur. Originality/value: By treating the perturbation as the second slow variable, the authors obtain that the MMOs are due to the canards in a supercritical case or in a subcritical case. This study can reveal the transition mechanism for multi-time scale characteristics in perturbed circuit. The information gained from such results can be extended to periodically perturbed circuits. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
223. Stabilization and Chaos Control of an Economic Model via a Time-Delayed Feedback Scheme.
- Author
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Hu, Yang and Hu, Guangping
- Subjects
ECONOMIC models ,HOPF bifurcations ,MATHEMATICAL models ,COMPUTER simulation - Abstract
This paper addresses the problem of chaos control in an economic mathematical dynamical model. By regarding the control variables as the bifurcation parameters, the stability of equilibria and the existence of Hopf bifurcations of the relevance feedback system are investigated, and the criterion of controllability for the chaotic system is obtained based on a time-delayed feedback control technique. Furthermore, numerical simulations are provided to demonstrate the feasibility of our methods and results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
224. Complex Dynamics Analysis and Chaos Control of a Fractional-Order Three-Population Food Chain Model.
- Author
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Cui, Zhuang, Zhou, Yan, and Li, Ruimei
- Subjects
FOOD chains ,PREDATION ,JACOBI operators ,STABILITY theory ,FRACTIONAL differential equations ,HOPF bifurcations ,POLYNOMIAL chaos - Abstract
The present study investigates the stability analysis and chaos control of a fractional-order three-population food chain model. Previous research has indicated that the predation relationship within a long-established predator–prey system can be influenced by factors such as the prey's fear of the predator and its carry-over effects. This study examines the state evolution of fractional-order systems and compares their dynamic behavior with integer-order systems. By utilizing the Routh–Hurwitz condition and the stability theory of fractional differential equations, this paper establishes the local stability conditions of the model through the application of the Jacobi matrix and eigenvalue method. Furthermore, the conditions for the Hopf bifurcation generation are determined. Subsequently, chaos control techniques based on the Lyapunov stability theory are employed to stabilize the unstable trajectory at the equilibrium point. The theoretical findings are validated through numerical simulations. These results enhance our understanding of the stability properties and chaos control mechanisms in fractional-order three-population food chain models. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
225. Dynamic Behavior of a Class of Six-Neuron Fractional BAM Neural Networks.
- Author
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Li, Weinan, Liao, Maoxin, Li, Dongsheng, Xu, Changjin, and Li, Bingbing
- Subjects
HOPF bifurcations - Abstract
In this paper, the stability and Hopf bifurcation of a six-neuron fractional BAM neural network model with multiple delays are considered. By transforming the multiple-delays model into a fractional-order neural network model with a delay through the variable substitution, we prove the conditions for the existence of Hopf bifurcation at the equilibrium point. Finally, our results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
226. Kinetic analysis of spike and wave discharge in a neural mass model.
- Author
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Wang, Zhihui and Xie, Manhong
- Subjects
WAVE analysis ,LIMIT cycles ,INTERNEURONS ,PYRAMIDAL neurons ,NEURAL inhibition ,HOPF bifurcations - Abstract
In the brain, feedforward inhibition is a fundamental regulator of balancing neural excitation and inhibition, and its dysfunction may cause epilepsy. In this paper, we investigate the influence of feedforward inhibition on absence seizures and its dynamical mechanisms based on a neural mass model. On the one hand, pyramidal neurons (PY), fast kinetic interneurons ( I fast ) and slow kinetic interneurons ( I slow ) form two feedforward inhibition pathways, which are the PY– I fast – I slow pathway and the PY– I slow – I fast pathway, respectively. When changing the synaptic strength in different pathways, the system shows simple oscillation state, spike and wave discharge (SWD), and multi-spike and wave discharge (m-SWD). On the other hand, the one-parameter bifurcation analysis reveals that the system develops fold bifurcations, Hopf bifurcations, fold bifurcations on limit cycle, and period doubling bifurcations when state transitions occur. In particular, when the system is in the bistable region, the dynamic state of this region is closely related to the stable limit cycle and stable fixed point. Therefore, feedforward inhibition pathways are indeed involved in the regulation of absence seizures, excitatory connections in both feedforward inhibition pathways are more effective than the inhibitory connections in the control of absence seizures. More interestingly, the feedforward inhibition pathway PY– I slow – I fast has a stronger regulation of absence seizures than PY– I fast – I slow . These results provide a theoretical basis for a more detailed understanding of the underlying mechanisms of neurological disorders. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
227. Hopf Bifurcation Analysis of a Housefly Model with Time Delay.
- Author
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Chang, Xiaoyuan, Gao, Xu, and Zhang, Jimin
- Subjects
HOPF bifurcations ,BIFURCATION theory ,HOUSEFLY ,EIGENVALUES - Abstract
The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov–LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu's global Hopf bifurcation theory, the existence of the global bifurcation is established under certain conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
228. ON THE DYNAMICS OF A FRACTIONAL-ORDER RICCATI DIFFERENTIAL EQUATION WITH PERTURBED DELAY.
- Author
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EL-SAYED, A. M. A., SALMAN, S. M., and ABDELFATTAH, A. A. F.
- Subjects
RICCATI equation ,DELAY differential equations ,HOPF bifurcations ,LYAPUNOV exponents ,BIFURCATION diagrams ,DISCRETE systems - Abstract
This paper studies the dynamics of a fractional-order Riccati differential equation with perturbed delay and introduces a novel concept of perturbed delay. The study focuses on understanding the behaviour of the solution through the application of analytical techniques to investigate the existence and uniqueness of the solution and its continuous dependence on initial conditions. Analyses of Hopf bifurcations and the local stability of fixed points are studied. The discrete system is generated by piecewise constant arguments in order to simulate the behaviour of the system under consideration. The local stability analysis of the fixed points of the discrete system is presented. Numerical simulations using bifurcation diagrams, Lyapunov exponents and phase diagrams are illustrated. This helps confirm our research and unearth more complex dynamics. The theoretical results of the fractional order Riccati differential equation with delay and its perturbed equation are compared. Our results show that, under specific conditions, the fractional-order Riccati differential equation with perturbed delay exhibits equivalent dynamical properties to the fractional-order Riccati differential equation with delay. [ABSTRACT FROM AUTHOR]
- Published
- 2023
229. Fractional-order PID control of tipping in network congestion.
- Author
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He, Jiajin, Xiao, Min, Lu, Yunxiang, Wang, Zhen, and Zheng, Wei Xing
- Subjects
PID controllers ,HOPF bifurcations ,TELECOMMUNICATION systems - Abstract
Tracing the rapid progress of communication network, the control of dynamic evolution of network has become a central issue. There are a lot of tipping phenomena in network congestion systems. Therefore, tipping control principally centres on traditional control policies, and some advanced control approaches need to be supplemented. In this paper, a fractional-order proportional-integral-derivative (PID) controller is introduced to a network congestion model to ponder corresponding bifurcation-induced tipping regulation. First, a fractional-order congestion model with fractional-order PID controller is constructed. Then the onset of the tipping induced by Hopf bifurcation of the uncontrolled model is studied. By contrast, the tipping point can be delayed under the controller for the controlled model. Some conditions under which Hopf bifurcation occurs are given. The stable and unstable ranges of control parameters for the controlled model are also deduced. At last, some simulated examples are given to verify the theoretical results and demonstrate the superiority of the controller in tipping regulation. Moreover, the bidirectional effects of the controller are displayed by manipulating the control parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
230. Dynamics of an IS-LM macroeconomic model with delay-dependent coefficients.
- Author
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Collera, Juancho A.
- Subjects
MACROECONOMIC models ,DELAY differential equations ,INTERNAL revenue ,HOPF bifurcations ,TAX rates ,LOCUS (Mathematics) - Abstract
In this paper, we propose and analyze an IS-LM macroeconomic model with delay-dependent coefficients. The model assumes that the tax revenues have two complementary components, one based on the current income and the other on a past income where the fixed discrete time delay arises. Moreover, we assume that the tax share on each component depends on the time delay, and thus the resulting model is a system of delay differential equations with delay-dependent coefficients. Previously, De Cesare and Sportelli (2005) studied a similar model but the tax shares that they used were fixed constants. They showed that the equilibrium point may undergo a sequence of alternated stability switches. This can be observed for example in the case with low tax rate and low share of delayed tax revenue where loci of Hopf bifurcation points form closed curves with some of these curves overlap, and the equilibrium is unstable inside these loci. Our proposed model introduces a new parameter μ in the tax share terms, and the case where μ = 0 captures the previously studied model with constant tax shares. We showed that increasing this new parameter results to decoupling and shrinking of the 'islands of instability', and eventually results to the absolute stability of the equilibrium. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
231. Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems.
- Author
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Barge, Héctor and Sanjurjo, José M. R.
- Subjects
HOPF bifurcations ,DYNAMICAL systems ,DISCRETE systems ,TOPOLOGY ,BIFURCATION diagrams ,BIFURCATION theory ,MATHEMATICS - Abstract
In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in [Math Processing Error] n -dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
232. Diffusion-driven instability of both the equilibrium solution and the periodic solutions for the diffusive Sporns-Seelig model.
- Author
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Xiang, Nan, Wan, Aying, and Lin, Hongyan
- Subjects
HOPF bifurcations ,BIFURCATION theory ,SPATIOTEMPORAL processes ,EQUILIBRIUM ,MATHEMATICS - Abstract
In this paper, a reaction-diffusion Sporn-Seelig model subject to homogeneous Neumann boundary condition in the one dimensional spatial open bounded domain is considered. Of our particular interests, we are concerned with diffusion-driven instability of both the positive constant equilibrium solution and the Hopf bifurcating spatially homogeneous periodic solutions. To strengthen our analytical results, we also include some numerical simulations. These results allow for the clearer understanding the mechanisms of the spatiotemporal pattern formations of this chemical reaction model. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
233. Stability Analysis of a Leslie–Gower Model with Strong Allee Effect on Prey and Fear Effect on Predator.
- Author
-
Liu, Tingting, Chen, Lijuan, Chen, Fengde, and Li, Zhong
- Subjects
ALLEE effect ,LOTKA-Volterra equations ,LIMIT cycles ,HOPF bifurcations ,PREDATORY animals ,COMPUTER simulation - Abstract
In this paper, we propose a Leslie–Gower predator–prey model with strong Allee effect on prey and fear effect on predator. We discuss the existence and local stability of equilibria by making full use of qualitative analytical theory. It is shown that the above system exhibits at most two positive equilibria and it can undergo a series of bifurcation phenomena. We indicate that the dynamical behavior of the model is closely related to the fear effect on predator. In detail, when the fear effect parameter p = p ∗ , the system will undergo degenerate Hopf bifurcation. There exist two limit cycles (the inner is stable and the outer is unstable). However, when p = p ∗ , the system will undergo degenerate Bogdanov–Takens bifurcation. Also, by numerical simulation, we conclude that the stronger the fear effect, the bigger the density of prey species. The above shows that fear effect on predator is beneficial to the persistence of the prey species. Our results can be seen as a complement to previous works [González-Olivares et al., 2011; Pal & Mandal, 2014]. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
234. NON-CHAOS-MEDIATED MIXED-MODE OSCILLATIONS IN AN EXTENDED HINDMARSH-ROSE NEURONAL OSCILLATOR WITH TIME DELAY.
- Author
-
Jiangang ZHANG, Lixiang WEI, Xinlei AN, and Mengran NAN
- Subjects
HOPF bifurcations ,OSCILLATIONS ,DYNAMICAL systems - Abstract
This paper proposes an extended neuron model with time delay. It aims to investigate the effect of time delay on the dynamical behavior of the system under different conditions. The existence of the Hopf bifurcation of the system and the stability of its periodic solution are proved by the central manifold theorem. Numerical results show that the system has abundant dynamical performance, including chaos, period-adding, and intermittent chaos. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
235. Global Hopf bifurcation for two zooplankton-phytoplankton model with two delays.
- Author
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Shi, Renxiang and Yang, Wenguo
- Subjects
HOPF bifurcations ,MARINE zooplankton ,LIMIT cycles ,FRACTALS ,SOLITONS ,GLOBAL studies - Abstract
In this paper, we study the global existence of a bifurcating periodic solution for a two zooplankton-phytoplankton model with two delays. First, we demonstrate that the bifurcating periodic solution exists when one delay increases and the other delay remains unchanged. Second, we give simulation to describe the bifurcating periodic solution when one delay increases. Our work answers the question in Sect. 5 (Shi and Yu in Chaos Solitons Fractals 100:62–73, 2017). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
236. Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect.
- Author
-
Shang, Zuchong and Qiao, Yuanhua
- Subjects
- *
FOOD chains , *TOP predators , *NONLINEAR dynamical systems , *GEOMETRIC approach , *HOPF bifurcations , *LIMIT cycles , *POPULATION density - Abstract
In this paper, a four-species food web model is formulated to investigate the influence of fear effect and nonlinear top predator harvesting on the dynamical behaviors. The global stability of the system at the interior equilibrium is explored by Li–Muldowney geometric approach. By applying the Sotomayor's theorem, it is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation. The conditions for the occurrence of Hopf bifurcation are established, and the stability of the bifurcating limit cycle is discussed by normal form theory. Finally, the numerical simulations are carried out. It is observed that the system presents chaotic dynamics, periodic window and chaotic attractors. Two distinct routes to chaos are discovered, one is period doubling cascade and the other is the generation and destruction of quasi-periodic states. Moreover, it is found that the fear effect can suppress fluctuations in population density to stabilize the system. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
237. Bifurcation analysis and chaos for a double-strains HIV coinfection model with intracellular delays, saturated incidence and Logistic growth.
- Author
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Chen, Wei, Zhang, Long, Wang, Ning, and Teng, Zhidong
- Subjects
- *
BASIC reproduction number , *MIXED infections , *HOPF bifurcations , *VIRAL load , *HIV infection transmission , *HIV - Abstract
In this paper, a class of virus-to-cell HIV model with intracellular delays, saturated incidence and Logistic growth is proposed to characterize the interaction between two types HIV strains, i.e., wild-type and drug-resistant strains. First, a series of threshold criteria on the locally and globally asymptotic stability of (infection-free, dominant, coexistence) equilibria are discussed based on the basic reproduction number R 0. Furthermore, a detailed Hopf bifurcation analysis is performed on the coexistence equilibrium using two delays as bifurcation parameters. We find that the Hopf bifurcations induced by double-strains are evidently different and more complicated than that of single strain, the former switches from stability (periodic branches) to un-stability (chaos) more frequently and earlier than the latter since double-strains would yield more pairs of imaginary roots in the characteristic equations. Meanwhile, the total viral load of double-strains would be higher than that of single-strain as well. The emergence of drug resistance imposes either negative or positive influences on the survival of wild-type strain, which would further facilitate the transmission of HIV. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
238. Hopf bifurcation and fixed-time stability of a reaction–diffusion echinococcosis model with mixed delays.
- Author
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Chen, Weixin, Xu, Xinzhong, and Zhang, Qimin
- Subjects
- *
HOPF bifurcations , *ECHINOCOCCOSIS , *NONLINEAR systems , *COMPUTER simulation - Abstract
In this paper, a model with spatial diffusion and mixed delays is presented to describe the spread of echinococcosis between dogs and livestock. Firstly, the local stability is investigated using the Routh–Hurwitz criterion. Furthermore, when considering time delays as bifurcation parameters, the conditions for the occurrence of Hopf bifurcation are discussed based on the linear approximation of the nonlinear system. Lastly, the fixed-time stability is studied under the implementation of appropriate control measures. Numerical simulations are provided to give a better understanding of the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
239. Spatiotemporal patterns in a diffusive resource–consumer model with distributed memory and maturation delay.
- Author
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Shen, Hao and Song, Yongli
- Subjects
- *
HOPF bifurcations , *MEMORY , *DIFFUSION coefficients - Abstract
In this paper, we propose a diffusive consumer–resource model in which the consumer is involved with spatiotemporal memory and the resource has maturation delay. Firstly, for the case without maturation delay, the influence of the spatiotemporal distributed memory on the stability of the positive steady state is investigated. It has been shown that memory delay can induce Turing bifurcation for the negative memory-based diffusion coefficient and induce Hopf bifurcation for the positive memory-based diffusion coefficient. Then the joint effect of the memory delay and the maturation delay on the stability of the positive steady state is investigated and it has been shown that the joint effect of the memory delay and the maturation delay can induce more complicated spatiotemporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our theoretical analysis results to a consumer–resource model with Holling-II type functional response to illustrate the existence of the different spatiotemporal patterns. • Propose a diffusive resource-consumer model with distributed memory and maturation delay. • Investigate the joint effect of the memory delay and the maturation delay on the spatiotemporal dynamics. • Find the spatially inhomogeneous spatial patterns and spatially inhomogeneous periodic patterns. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
240. Bifurcations and steady states of a predator–prey model with strong Allee and fear effects.
- Author
-
Chen, Mengxin, Li, Xuezhi, and Wu, Ranchao
- Subjects
- *
ALLEE effect , *HOPF bifurcations - Abstract
In this paper, the predator–prey model with strong Allee and fear effects is considered. The existence of the equilibria and their stability are established. Especially it is found that there is an interesting degenerate point, which is a cusp point with codimension 2 or higher codimension, or an attracting (repelling)-type saddle-node, subject to different conditions. Then the Hopf bifurcation and its direction, the saddle-node bifurcation and the Bogdanov–Tankens bifurcation are further explored. Afterwards, with the help of the energy estimates and the Leray–Schauder degree, the nonexistence and existence of the nonconstant steady states of the model are presented. From the obtained results, we find that strong Allee effect will cause the per capita growth rate of prey species from negative to positive; both the fear and Allee effects could affect the existence of equilibria and bifurcations; meanwhile, the diffusion rates will affect the existence of the nonconstant steady states. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
241. Bifurcation analysis of a delayed reaction–diffusion–advection Nicholson's blowflies equation.
- Author
-
Tan, Mengfan, Wei, Chunjin, and Wei, Junjie
- Subjects
- *
BLOWFLIES , *HOPF bifurcations , *ADVECTION , *EQUATIONS - Abstract
In this paper, we investigate the dynamics of a reaction-diffusion Nicholson's blowflies equation with advection. The stability of positive steady state and existence of Hopf bifurcation are obtained by analyzing the distribution of the eigenvalues. Moreover, by using the center manifold theory and normal form method, an explicit algorithm for determining the direction and stability of the Hopf bifurcation is derived. Meanwhile, we find out that the bifurcation value is increasing with respect to the advection rate. Finally, numerical results demonstrate that the advection term causes the population to move from upstream to downstream, which also indicates that advection term plays a key role in the description and interpretation of some common natural phenomena. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
242. Methodology for Voltage Stability Analysis Using Hopf Bifurcation and Continuation Power Flow Simulator.
- Author
-
Roque, Matheus M. and Pessanha, José Eduardo O.
- Subjects
HOPF bifurcations ,JACOBIAN matrices ,COMPUTER software ,EIGENVECTORS ,EIGENVALUES - Abstract
The search for the Hopf bifurcation point in power systems can be made as the load is increased by small steps, and a power flow is solved for every load until a pair of purely imaginary eigenvectors has been found (zero real part). However, a search through successive power flows is time-consuming and does not guarantee that the Hopf bifurcation point will be found. This paper proposes a methodology and strategies that mitigate these problems. To increase the possibility of finding the Hopf bifurcation point, a continuation power flow is used to stablish search paths as the loading is incremented according to a fraction of the maximum loading point of the power system. It is only at specific converged continuation power flow that the dynamic state Jacobian matrix is constructed and has its eigenvalues computed. To facilitate the understanding and application of the proposal, it is used the MATPOWER (version 7.0) computer program and two available power systems. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
243. Nonlinear magneto-electric response of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic excitation.
- Author
-
Xu, J., Kong, Y. X., Wang, H. L., and Zhu, Z. W.
- Subjects
MAGNETOSTRICTIVE devices ,PIEZOELECTRIC ceramics ,MAGNETOELECTRIC effect ,HOPF bifurcations ,DYNAMIC models ,NONLINEAR differential equations ,HARMONIC analysis (Mathematics) - Abstract
Nonlinear magneto-electric response characteristics of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic magnetic fields are studied in this paper. Van der Pol nonlinear differential items are introduced to explain the hysteresis phenomena of both giant magnetostrictive material and piezoelectric ceramics. The nonlinear dynamic model of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic magnetic fields is developed. The expression of dynamic response of the system is obtained, and the bifurcation characteristics of the system are analyzed. The results of this paper are helpful for optimal design and improvement of giant magnetostrictive-piezoelectric composite sensors. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
244. Stability and Bifurcation Analysis of a Nonlinear Rotating Cantilever Plate System.
- Author
-
Chen, Shuping, Zhang, Danjin, and Qian, Youhua
- Subjects
NONLINEAR analysis ,CANTILEVERS ,HOPF bifurcations ,CENTRIFUGAL force ,NONLINEAR systems ,TORUS - Abstract
This paper investigates the bifurcation behavior and the stability of the rotating cantilever rectangular plate that is subjected to varying speed and centrifugal force. The local stability of the degenerated equilibrium of nonlinear system with symmetry is observed after analyzing the corresponding characteristic equation. In addition to complex phenomena such as static bifurcation and Hopf bifurcation, the 2-D torus bifurcation is investigated in this paper. Thereafter, the steady-state solutions and stability region are obtained using the center manifold theory and normal form method. Finally, numerical simulations are conducted to show the nonlinear dynamical behaviors of the rotating cantilever rectangular plate. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
245. Bifurcations due to different delays of high-order fractional neural networks.
- Author
-
Huang, Chengdai and Cao, Jinde
- Subjects
HOPF bifurcations ,LEAKAGE - Abstract
This paper expounds the bifurcations of two-delayed fractional-order neural networks (FONNs) with multiple neurons. Leakage delay or communication delay is viewed as a bifurcation parameter, stability zones and bifurcation conditions with respect to them are commendably established, respectively. It declares that both leakage delay and communication delay immensely influence the stability and bifurcation of the developed FONNs. The explored FONNs illustrate superior stability performance if selecting a lesser leakage delay or communication delay, and Hopf bifurcation generates once they overstep their critical values. The verification of the feasibility of the developed analytic results is implemented via numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
246. Hopf and Zero-Hopf Bifurcation Analysis for a Chaotic System.
- Author
-
Husien, Ahmad Muhamad and Amen, Azad Ibrahim
- Subjects
- *
HOPF bifurcations , *LIMIT cycles , *ORDINARY differential equations , *NONLINEAR differential equations , *ELECTRONIC circuits , *ORBITS (Astronomy) - Abstract
In this paper, we investigate a quadratic chaotic system modeling self-excited and hidden attractors which is described by a system of three nonlinear ordinary differential equations with three real parameters. The primary goal is to establish the existence of two limit cycles that bifurcate based on the system's nature as an electronic circuits model, specifically via Hopf bifurcation. Notably, the application of the first and second Lyapunov coefficients is utilized to demonstrate the bifurcation of two limit cycles from an equilibrium point near a Hopf critical point. Furthermore, employing the first-order averaging theory enables us to confirm the presence of unstable periodic orbits originating from the zero-Hopf equilibrium. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
247. Rich Dynamics in a Hindmarsh–Rose Neuronal Model with Time Delay.
- Author
-
Jiao, Xubin and Liu, Xiuxiang
- Subjects
- *
HOPF bifurcations , *EQUILIBRIUM , *COMPUTER simulation - Abstract
This paper presents the stability and bifurcation of the Hindmarsh–Rose neuronal model with time delay. First, we discuss the existence and stability of the equilibria, revealing that the system can have a maximum of three equilibria which exhibit always stable, always unstable, and stability switching dynamics, depending on the stability of the equilibria when there is no time delay. Furthermore, an explicit formula for the time delay at which Hopf bifurcation occurs is derived, and the direction and stability of the Hopf bifurcation are also given. Finally, numerical simulations are carried out to support our theoretical results. We find that due to the existence of time delay, our system can exhibit many interesting dynamical behaviors depending on the number of equilibria and the increase in time delay. For instance, with increasing time delay, bistability transitions to the coexistence of a periodic solution and a stable equilibrium, followed by the emergence of quasi-periodic motion alongside stable equilibria, and eventually leading to chaotic motion coexisting with a stable equilibrium. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
248. Dynamics of a High-Speed Railway Wheelset with Two Time Delays in Primary Suspension Dampers.
- Author
-
Li, Yue, Huang, Caihong, Shi, Huailong, Zeng, Jing, and Cao, Hongjun
- Subjects
- *
LIMIT cycles , *HIGH speed trains , *HOPF bifurcations , *PERIODIC motion - Abstract
A two-degree-of-freedom nonlinear high-speed railway wheelset model with two time delays in the lateral and yaw dampers is studied. The aim is to investigate the effect of time delays on stability and Hopf bifurcation characteristics of the wheelset model. The local stability of the trivial equilibrium under different time delay conditions is qualitatively analyzed. Analytical studies reveal that the wheelset model undergoes stability switches with the variation of the time delays. The stability switches correspond to Hopf bifurcations that occur when the time delays cross critical values. Furthermore, properties of Hopf bifurcation including direction and stability of bifurcating limit cycles are studied by using the normal form theory and the center manifold theorem. Our findings indicate that time delays in both lateral dampers and yaw dampers influence the stability and direction of Hopf bifurcation. Additionally, the numerical results show that time delays in the lateral and yaw dampers not only affect the amplitude of the hunting motion of the wheelset but also the periodic and chaotic motions. If the time delays gradually increase, the wheelset will vibrate irregularly with large lateral displacements. The analytical results presented in this paper offer a theoretical reference for the stability design of wheelsets. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
249. Hopf Bifurcation and Turing Instability of a Delayed Diffusive Zooplankton–Phytoplankton Model with Hunting Cooperation.
- Author
-
Meng, Xin-You and Xiao, Li
- Subjects
- *
HOPF bifurcations , *PARTIAL differential equations , *COMPETITION (Biology) , *BIFURCATION theory , *HUNTING , *COOPERATION - Abstract
In this paper, a diffusive zooplankton–phytoplankton model with time delay and hunting cooperation is established. First, the existence of all positive equilibria and their local stability are proved when the system does not include time delay and diffusion. Then, the existence of Hopf bifurcation at the positive equilibrium is proved by taking time delay as the bifurcation parameter, and the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by using the center manifold theorem and the normal form theory in partial differential equations. Next, according to the theory of Turing bifurcation, the conditions for the occurrence of Turing bifurcation are obtained by taking the intraspecific competition rate of the prey as the bifurcation parameter. Furthermore, the corresponding amplitude equations are discussed by using the standard multi-scale analysis method. Finally, some numerical simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
250. Slow–Fast Dynamics of a Piecewise-Smooth Leslie–Gower Model with Holling Type-I Functional Response and Weak Allee Effect.
- Author
-
Wu, Xiao and Xie, Feng
- Subjects
- *
ALLEE effect , *HOPF bifurcations , *PREDATION , *FOOD quality , *PARAMETERS (Statistics) , *GLOBAL analysis (Mathematics) , *DIFFERENTIABLE dynamical systems , *LIMIT cycles , *LOTKA-Volterra equations - Abstract
The slow–fast Leslie–Gower model with piecewise-smooth Holling type-I functional response and weak Allee effect is studied in this paper. It is shown that the model undergoes singular Hopf bifurcation and nonsmooth Hopf bifurcation as the parameters vary. The theoretical analysis implies that the predator's food quality and Allee effect play an important role and lead to richer dynamical phenomena such as the globally stable equilibria, canard explosion phenomenon, a hyperbolically stable relaxation oscillation cycle enclosing almost two canard cycles with different stabilities and so on. Moreover, the predator and prey will coexist as multiple steady states or periodic oscillations for different positive initial populations and positive parameter values. Finally, we present some numerical simulations to illustrate the theoretical analysis such as the existence of one, two or three limit cycles. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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