scholarly journals Hopf bifurcation for an SIR model with age structure

2021 ◽  
Author(s):  
HUI CAO ◽  
Dongxue Yan ◽  
Xiaxia Xu
Keyword(s):  
Cauchy Problem ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Age Structure ◽  
Equilibrium Points ◽  
Sir Model ◽  
Numerical Examples ◽  
System Parameters ◽  
Stability And Instability ◽  
Densely Defined

This paper deals with an SIR model with age structure of infected individuals. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system. The criteria for both stability and instability involving system parameters are obtained. Bifurcation analysis indicates that the system with age structure exhibits Hopf bifurcation which is the main result of this paper. Finally, some numerical examples are provided to illustrate our obtained results.

Hopf Bifurcation Analysis of a Three-Stage-Structured Prey-Predator System with Multi-Delays

2013 ◽  
Vol 756-759 ◽  
pp. 2857-2862
Author(s):  
Shun Yi Li ◽  
Wen Wu Liu
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Characteristic Equations ◽  
Numerical Examples ◽  
Predator Model ◽  
Predator System

A three-stage-structured prey-predator model with multi-delays is considered. The characteristic equations and local stability of the equilibrium are analyzed, and the conditions for the positive equilibrium occurring Hopf bifurcation are obtained by applying the theorem of Hopf bifurcation. Finally, numerical examples and brief conclusion are given.

Stability and Hopf bifurcation analysis of a new four-dimensional hyper-chaotic system

2020 ◽  
Vol 34 (29) ◽  
pp. 2050327
Author(s):  
Liangqiang Zhou ◽  
Ziman Zhao ◽  
Fangqi Chen
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Bifurcation Theory ◽  
Center Manifold ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Local Dynamic ◽  
Chaotic Motions ◽  
System Parameters ◽  
Lyapunov Coefficient

With both analytical and numerical methods, local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional hyper-chaotic system are studied in this paper. All the equilibrium points and their stability conditions are obtained with the Routh–Hurwitz criterion. It is shown that there may exist one, two, or three equilibrium points for different system parameters. Via Hopf bifurcation theory, parameter conditions leading to Hopf bifurcation is presented. With the aid of center manifold and the first Lyapunov coefficient, it is also presented that the Hopf bifurcation is supercritical for some certain parameters. Finally, numerical simulations are given to confirm the analytical results and demonstrate the chaotic attractors of this system. It is also shown that the system may evolve chaotic motions through periodic bifurcations or intermittence chaos while the system parameters vary.

scholarly journals Hopf Bifurcation Analysis in a Tabu Learning Neuron Model with Two Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Yingguo Li
Keyword(s):  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Bifurcation Analysis ◽  
Neuron Model ◽  
Dynamical Behavior ◽  
Bifurcation Parameter ◽  
Nonlinear Dynamical ◽  
Numerical Examples ◽  
Two Delays

We consider the nonlinear dynamical behavior of a tabu leaning neuron model with two delays. By choosing the sum of the two delays as a bifurcation parameter, we prove that Hopf bifurcation occurs in the neuron. Some numerical examples are also presented to verify the theoretical analysis.

scholarly journals Bifurcation Analysis of a Model of Cancer

2016 ◽  
Vol 12 (3) ◽  
pp. 67 ◽  
Author(s):  
Abdo M. Al-Mahdi ◽  
Mustafa Q. Khirallah
Keyword(s):  
Numerical Analysis ◽  
Bifurcation Analysis ◽  
System Parameter ◽  
Steady States ◽  
Cancer Model ◽  
Unknown Parameters ◽  
Numerical Examples ◽  
System Parameters ◽  
Parameter Values

In this paper, we study the bifurcation of a cancer model with completely unknown parameters. The bifurcation analysis of the biologically feasible steady-states of this model will be discussed. It is proved that the system appears to exhibit many cases of bifurcation for some ranges of system parameters. Numerical analysis and extensive numerical examples of the bifurcation for some ranges were carried out for various system parameter values and different initial densities.

scholarly journals The Dynamical Analysis of Computer Viruses Model with Age Structure and Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hui Cao ◽  
Si Wang ◽  
Dongxue Yan ◽  
Hongwu Tan ◽  
Hemiao Xu
Keyword(s):  
Age Structure ◽  
Reproduction Number ◽  
Dynamical Analysis ◽  
Acquired Immunity ◽  
Computer Viruses ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Stability And Instability ◽  
Theoretical Results ◽  
The Basic Reproduction Number

This paper deals with the dynamical behaviors for a computer viruses model with age structure, where the loss of the acquired immunity and delay are incorporated. Through some rigorous analyses, an explicit formula for the basic reproduction number of the model is calculated, and some results about stability and instability of equilibria for the model are established. These findings show that the age structure and delay can produce Hopf bifurcation for the computer viruses model. The numerical examples are executed to validate the theoretical results.

Global dynamics for a TB transmission model with age-structure and delay

2020 ◽  
Vol 13 (07) ◽  
pp. 2050055
Author(s):  
Dongxue Yan ◽  
Hui Cao ◽  
Suxia Zhang
Keyword(s):  
Explicit Formula ◽  
Global Attractor ◽  
Age Structure ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Model ◽  
Global Dynamics ◽  
Numerical Examples ◽  
Stability And Instability ◽  
The Basic Reproduction Number

This paper deals with the global dynamics of a tuberculosis (TB) model with age-structure and delay. We perform some rigorous analyses for the model, including presenting an explicit formula for the basic reproduction number of the model, addressing the persistence of the solution semi-flow and the existence of the global attractor. Based on these analyses, we establish some results on stability and instability of equilibrium of the system. Finally, some numerical examples are provided to illustrate our obtained results.

scholarly journals The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ping Bi ◽  
Zijian Liu ◽  
Mutei Damaris Muthoni ◽  
Jianhua Pang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Normal Form ◽  
Bifurcation Analysis ◽  
Center Manifold ◽  
Tumor Model ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Existence And Stability ◽  
Discrete Delays

This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with discrete delays. The properties of the bifurcated periodic solutions are studied by using the normal form on the center manifold. Numerical examples and simulations are given to illustrate the bifurcation analysis and the obtained results.

Hopf Bifurcation Analysis in a Modified Optically Injected Semiconductor Lasers Model

2014 ◽  
Vol 631-632 ◽  
pp. 254-260
Author(s):  
Jiang Ang Zhang ◽  
Wen Ju Du ◽  
Kutorzi Edwin Yao
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Semiconductor Lasers ◽  
Bifurcation Analysis ◽  
Autonomous System ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Bifurcation Parameter ◽  
Numerical Example ◽  
The Stability

In this paper, a modified optically injected semiconductor lasers model is studied in detail. More precisely, we study the stability of the equilibrium points and basic dynamic properties of the autonomous system by means of nonlinear dynamics theory. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the stability and the conditions for generating Hopf bifurcation of the equilibria are derived. Then, a numerical example is given.

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