Stability and Hopf bifurcation analysis of flux neuron model with double time delays

2022 ◽  
Author(s):  
Lixiang Wei ◽  
Jiangang Zhang ◽  
Xinlei An ◽  
Mengran Nan ◽  
Shuai Qiao
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Neuron Model ◽  
Double Time

Bifurcation analysis of a fractional-order SIQR model with double time delays

2020 ◽  
Vol 13 (07) ◽  
pp. 2050067
Author(s):  
Shouzong Liu ◽  
Ling Yu ◽  
Mingzhan Huang
Keyword(s):  
Hopf Bifurcation ◽  
Convergence Rate ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Oscillatory System ◽  
Endemic Equilibrium ◽  
Nonlinear Incidence Rate ◽  
Double Time ◽  
The Stability

In this paper, a fractional-order delayed SIQR model with nonlinear incidence rate is investigated. Two time delays are incorporated in the model to describe the incubation period and the time caused by the healing cycle. By analyzing the associated characteristic equations, the stability of the endemic equilibrium and the existence of Hopf bifurcation are obtained in three different cases. Besides, the critical values of time delays at which a Hopf bifurcation occurs are obtained, and the influence of the fractional order on the dynamics behavior of the system is also investigated. Numerically, it has been shown that when the endemic equilibrium is locally stable, the convergence rate of the system becomes slower with the increase of the fractional order. Besides, our studies also imply that the decline of the fractional order may convert a oscillatory system into a stable one. Furthermore, we find in all these three cases, the bifurcation values are very sensitive to the change of the fractional order, and they decrease with the increase of the order, which means the Hopf bifurcation gradually occurs in advance.

Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays

2020 ◽  
Vol 131 ◽  
pp. 109483 ◽  
Author(s):  
Zizhen Zhang ◽  
Soumen Kundu ◽  
Jai Prakash Tripathi ◽  
Sarita Bugalia
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Time Delays ◽  
Multiple Time ◽  
Multiple Time Delays

Hopf Bifurcation of a Type of Neuron Model with Multiple Time Delays

2019 ◽  
Vol 29 (12) ◽  
pp. 1950163 ◽  
Author(s):  
Suqi Ma
Keyword(s):  
Hopf Bifurcation ◽  
Parameter Space ◽  
Time Delays ◽  
Neuron Model ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Geometrical Scheme ◽  
Delay Differential ◽  
Two Parameter

By applying a geometrical scheme developed to tackle the eigenvalue problem of delay differential equations with multiple time delays, Hopf bifurcation of Hopfield neuron model is analyzed in two-parameter space. By the introduction of two new angles, the calculation of imaginary roots is carried out analytically and effectively. By increasing the parameter to cross over the Hopf bifurcation lines, the stability switching direction is confirmed. The method is a useful tool to show the partition of stable and unstable regions in two-parameter space and detect double Hopf bifurcation further. The typified dynamical behaviors based on nearby double Hopf points are analyzed by applying the normal form technique and center manifold method.

Hopf bifurcation analysis of a tumor virotherapy model with two time delays

2020 ◽  
Vol 553 ◽  
pp. 124266 ◽  
Author(s):  
Hui-zhong Li ◽  
Xiang-dong Liu ◽  
Rui Yan ◽  
Cheng Liu
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Time Delays
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