The stochastic Hopf bifurcation analysis in Brusselator system with random parameter

2012 ◽  
Vol 219 (1) ◽  
pp. 306-319 ◽  
Author(s):  
Shaojuan Ma
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Random Parameter ◽  
Stochastic Hopf Bifurcation

scholarly journals Hopf Bifurcation of Compound Stochastic van der Pol System

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Shaojuan Ma ◽  
Qianling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Theory ◽  
Noise Intensity ◽  
Gaussian White Noise ◽  
Random Parameter ◽  
Critical Value ◽  
Deterministic System ◽  
Bifurcation Parameter ◽  
Van Der Pol ◽  
Stochastic Hopf Bifurcation

Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L) expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strengthδand noise intensityσon stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increasedδcan relocate the critical value of bifurcation parameter forward while increasedσmakes it backward and the influence ofδis more sensitive thanσ. The results are verified by numerical simulations.

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term

2018 ◽  
Vol 313 ◽  
pp. 306-315 ◽  
Author(s):  
Swati Tyagi ◽  
Subit K Jain ◽  
Syed Abbas ◽  
Shahlar Meherrem ◽  
Rajendra K Ray
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Network Model ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Neuron Network ◽  
Diffusion Term

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

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.

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