Local and global Hopf bifurcation in a neutral population model with age structure

2019 ◽  
Vol 42 (14) ◽  
pp. 4747-4764 ◽  
Author(s):  
Daifeng Duan ◽  
Ben Niu ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Age Structure ◽  
Population Model ◽  
Global Hopf Bifurcation

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.

Global Hopf Bifurcation in a Phytoplankton–Zooplankton System with Delay and Diffusion

2021 ◽  
Vol 31 (08) ◽  
pp. 2150114
Author(s):  
Ming Liu ◽  
Jun Cao ◽  
Xiaofeng Xu
Keyword(s):  
Hopf Bifurcation ◽  
Global Existence ◽  
Upper And Lower Solutions ◽  
Positive Periodic Solutions ◽  
Global Hopf Bifurcation ◽  
System With Delay ◽  
Local Hopf Bifurcation ◽  
Distribution Of Eigenvalues ◽  
The Stability ◽  
And Diffusion

In this paper, the dynamics of a phytoplankton–zooplankton system with delay and diffusion are investigated. The positivity and persistence are studied by using the comparison theorem and upper and lower solutions method. The stability of steady states and the existence of local Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. And the global existence of positive periodic solutions is established by using the global Hopf bifurcation result given by Wu [1996]. Finally, some numerical simulations are carried out to illustrate the analytical results.

Periodic Solutions of a Delayed Eco-Epidemiological Model with Infection-Age Structure and Holling Type II Functional Response

2020 ◽  
Vol 30 (01) ◽  
pp. 2050011 ◽  
Author(s):  
Peng Yang ◽  
Yuanshi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Age Structure ◽  
Epidemiological Model ◽  
Type Ii ◽  
Epidemic Disease ◽  
Semilinear Equations ◽  
Infection Age ◽  
Coexistence Equilibrium ◽  
Type Ii Functional Response

This paper is devoted to the study of a new delayed eco-epidemiological model with infection-age structure and Holling type II functional response. Firstly, the disease transmission rate function among the predator population is treated as the piecewise function concerning the incubation period [Formula: see text] of the epidemic disease and the model is rewritten as an abstract nondensely defined Cauchy problem. Besides, the prerequisite which guarantees the presence of the coexistence equilibrium is achieved. Secondly, via utilizing the theory of integrated semigroup and the Hopf bifurcation theorem for semilinear equations with nondense domain, it is found that the model exhibits a Hopf bifurcation near the coexistence equilibrium, which suggests that this model has a nontrivial periodic solution that bifurcates from the coexistence equilibrium as the bifurcation parameter [Formula: see text] crosses the bifurcation critical value [Formula: see text]. That is, there is a continuous periodic oscillation phenomenon. Finally, some numerical simulations are shown to support and extend the analytical results and visualize the interesting phenomenon.

scholarly journals Bifurcation of a Cohen-Grossberg Neural Network with Discrete Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Qiming Liu ◽  
Wang Zheng
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Hopf Bifurcations ◽  
Bifurcation Parameter ◽  
Explicit Formulas ◽  
Global Hopf Bifurcation ◽  
Discrete Delays ◽  
Bifurcation And Stability

A simple Cohen-Grossberg neural network with discrete delays is investigated in this paper. The existence of local Hopf bifurcations is first considered by choosing the appropriate bifurcation parameter, and then explicit formulas are given to determine the direction of Hopf bifurcation and stability of the periodic solutions. Moreover, a set of sufficient conditions are given to guarantee the global Hopf bifurcation. Numerical simulations are given to illustrate the obtained results.

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