scholarly journals Hopf bifurcation analysis and control of three-dimensional Prescott neuron model

2016 ◽  
Vol 18 (6) ◽  
pp. 4105-4115 ◽  
Author(s):  
Jiang Wang ◽  
Chunhua Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Neuron Model ◽  
Three Dimensional ◽  
And Control

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

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.

Hopf bifurcation analysis of a tabu learning two-neuron model

2006 ◽  
Vol 29 (1) ◽  
pp. 190-197 ◽  
Author(s):  
Yi Li ◽  
Xiaobing Zhou ◽  
Yue Wu ◽  
Mingtian Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Neuron Model

Stability analysis and Hopf bifurcation based on time delay neurons under electromagnetic fields

2021 ◽  
Author(s):  
Lixiang Wei ◽  
Jiangang Zhang ◽  
Xinlei An ◽  
Mengran Nan ◽  
Shuai Qiao
Keyword(s):  
Membrane Potential ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Electromagnetic Fields ◽  
Neuron Model ◽  
Neurological Diseases ◽  
Three Dimensional ◽  
External Electromagnetic Fields ◽  
The Stability ◽  
Bifurcation Structures

Neurons contain a large number of ions inside and outside the cell, and the transmembrane currents formed by the movement of these ions cause membrane potential fluctuations and induce electromagnetism inside and outside the cell. In addition, any change in external electromagnetic fields can cause changes in the membrane potential of the neurons. Therefore, based on the three-dimensional Hindmarsh — Rose (HR) neuron model, a five-dimensional neuron model with time delay is developed in this paper by introducing flux and electric field variables and considering the resulting time delay. First, the Hopf bifurcation theory is used to demonstrate the local stability of the system at the equilibrium point at different time delays. Then, the stability of the Hopf bifurcation and its direction are proved by using the central flow shape theorem. Finally, the existence of the Hopf bifurcation is proved using the phase diagram and the bifurcation diagram, and the effects of several important parameters on the model are investigated by numerical simulations using time series plots, ISI bifurcation plots and two-parameter bifurcation plots. The model is found to be accompanied by chaotic and chaos-free plus-periodic bifurcation structures, mixed-mode discharges and other phenomena. Also, its discharge pattern can be controlled after adding time delay. The results of this paper provide help to the pathogenic mechanism and control of neurological diseases.

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