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

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.

BIFURCATION ANALYSIS OF TIME-DELAY CONTROL SYSTEMS WITH SATURATION

1999 ◽  
Vol 09 (06) ◽  
pp. 1089-1109 ◽  
Author(s):  
DANIEL J. PAGANO ◽  
ENRIQUE PONCE ◽  
JAVIER ARACIL
Keyword(s):  
Time Delay ◽  
Frequency Domain ◽  
Control Systems ◽  
Bifurcation Analysis ◽  
Global Perspective ◽  
Frequency Domain Methods ◽  
Frequency Domain Approach ◽  
Theoretical Results ◽  
Delay Control Systems

A frequency domain approach to the bifurcation analysis of time-delay SISO control systems with saturation is proposed. Generic bifurcations to be expected for these systems are emphasized. The main goal is to give a classification of system behavior modes that are relevant for stability studies, reaching a global perspective of the parameter space. The classification is obtained through the bifurcation analysis, which is implemented by frequency domain methods that are well known to the control systems engineers. Some specific cases are analyzed with this methodology. The theoretical results are in agreement with numerical simulations.

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