system with delay
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2021 ◽  
Vol 2086 (1) ◽  
pp. 012109
Author(s):  
E G Fedorov ◽  
I Yu Popov

Abstract In this work an analytical and numerical analysis of the limiting behaviors of a system consisting of a pair of biological neurons was carried out. In this case connection between neurons will occur with a delay. As a neuron model, the FitzHugh-Nagumo model was chosen as a model that can reproduce many dynamic behaviors of a real neuron and, at the same time, is not very complex computationally.


2021 ◽  
Vol 31 (12) ◽  
pp. 2150184
Author(s):  
Renxiang Shi

In this paper, we study the dynamics of phytoplankton–zooplankton system with delay, where delay means that releasing toxin for phytoplankton is not instantaneous. First, we prove the positivity and boundedness of solutions, discuss the Hopf bifurcation caused by delay. Furthermore, we study the property of Hopf bifurcation by center manifold and normal form. Then, we study the global existence of bifurcated periodic solution. Finally by simulation, we show the influence of delay, disease spread and recovery from infected to susceptible on the dynamics of phytoplankton–zooplankton system.


2021 ◽  
Author(s):  
Zihao Cheng ◽  
Dong Yue ◽  
Songlin Hu ◽  
Yulong Xu

2021 ◽  
Vol 1964 (2) ◽  
pp. 022023
Author(s):  
S. Shyamala ◽  
K. Suresh ◽  
S.R. Anantha Lakshmi

2021 ◽  
Vol 31 (08) ◽  
pp. 2150114
Author(s):  
Ming Liu ◽  
Jun Cao ◽  
Xiaofeng Xu

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.


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