Hopf bifurcation for maps: a frequency-domain approach

2002 ◽  
Vol 49 (3) ◽  
pp. 281-288 ◽  
Author(s):  
M.B. D'Amico ◽  
J.L. Moiola ◽  
E.E. Paolini
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
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.

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

HOPF BIFURCATION IN A CALCIUM OSCILLATION MODEL AND ITS CONTROL: FREQUENCY DOMAIN APPROACH

2013 ◽  
Vol 23 (01) ◽  
pp. 1350012 ◽  
Author(s):  
YU CHANG ◽  
LILI ZHOU ◽  
JINLIANG WANG
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Periodic Orbits ◽  
Harmonic Balance ◽  
Bifurcation Theory ◽  
Harmonic Balance Method ◽  
Calcium Oscillation ◽  
Control Frequency ◽  
Oscillation Model ◽  
Frequency Domain Approach

The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

CHARACTERIZATION OF DYNAMIC BIFURCATIONS IN THE FREQUENCY DOMAIN

2002 ◽  
Vol 12 (01) ◽  
pp. 87-101 ◽  
Author(s):  
GRISELDA R. ITOVICH ◽  
JORGE L. MOIOLA
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Building Blocks ◽  
Hopf Bifurcations ◽  
Frequency Domain Approach ◽  
Dynamic Bifurcations ◽  
Bifurcation Behavior

In this paper dynamical systems with certain degenerate Hopf bifurcations are considered. An analysis of the bifurcation behavior is proposed using several tools from the frequency domain approach. The analyzed bifurcations are the building blocks to understand the multiplicity of Hopf bifurcation points and to propose certain strategies in the future for controlling the bifurcation behavior in nonlinear systems.

scholarly journals A frequency‐domain approach for damage detection in welded structures

2021 ◽  
Author(s):  
Camilla Ronchei ◽  
Sabrina Vantadori ◽  
Andrea Carpinteri ◽  
Ignacio Iturrioz ◽  
Roberto Issopo Rodrigues ◽  
...  
Keyword(s):  
Damage Detection ◽  
Frequency Domain ◽  
Welded Structures ◽  
Frequency Domain Approach

A frequency domain approach to residual generation for the industrial actuator benchmark

1995 ◽  
Vol 3 (12) ◽  
pp. 1747-1750 ◽  
Author(s):  
E. Alcorta García ◽  
B. Köppen-Seliger ◽  
P.M. Frank
Keyword(s):  
Frequency Domain ◽  
Frequency Domain Approach ◽  
Residual Generation
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