Hopf bifurcation analysis on a two-neuron system in the frequency domain

2003 ◽  
Author(s):  
Shaowen Li ◽  
Shaorong Li ◽  
Xiaofeng Liao
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Bifurcation Analysis ◽  
Neuron System

STABILITY AND HOPF BIFURCATION ON A TWO-NEURON SYSTEM WITH TIME DELAY IN THE FREQUENCY DOMAIN

2007 ◽  
Vol 17 (04) ◽  
pp. 1355-1366 ◽  
Author(s):  
WENWU YU ◽  
JINDE CAO
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Frequency Domain ◽  
Harmonic Balance ◽  
Neuron System ◽  
Bifurcation Theorem ◽  
Nyquist Criterion ◽  
The Stability ◽  
Frequency Domain Approach ◽  
System With Time Delay

In this paper, a general two-neuron model with time delay is considered, where the time delay is regarded as a parameter. It is found that Hopf bifurcation occurs when this delay passes through a sequence of critical value. By analyzing the characteristic equation and using the frequency domain approach, the existence of Hopf bifurcation is determined. The stability of bifurcating periodic solutions are determined by the harmonic balance approach, Nyquist criterion and the graphic Hopf bifurcation theorem. Numerical results are given to justify the theoretical analysis.

Frequency-Domain Approach to Hopf Bifurcation Analysis

10.1142/11418 ◽  
2019 ◽  
Author(s):  
Franco Sebastián Gentile ◽  
Jorge Luis Moiola ◽  
Guanrong Chen
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Bifurcation Analysis ◽  
Frequency Domain Approach

The Hopf bifurcation analysis on a time-delayed recurrent neural network in the frequency domain

2010 ◽  
Vol 73 (4-6) ◽  
pp. 991-1005 ◽  
Author(s):  
Amirhossein Hajihosseini ◽  
Gholam Reza Rokni Lamooki ◽  
Babak Beheshti ◽  
Farzaneh Maleki
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Recurrent Neural Network ◽  
Bifurcation Analysis

Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays

2016 ◽  
Vol 85 (2) ◽  
pp. 1039-1051 ◽  
Author(s):  
Esra Karaoğlu ◽  
Enes Yılmaz ◽  
Hüseyin Merdan
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Distributed Delays ◽  
Neuron System
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