Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback

2015 ◽  
Vol 24 (1) ◽  
pp. 014501 ◽  
Author(s):  
Shuang Liu ◽  
Shuang-Shuang Zhao ◽  
Zhao-Long Wang ◽  
Hai-Bin Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Electromechanical Coupling ◽  
Coupling System ◽  
System With Time Delay

scholarly journals Bifurcation Analysis of a Fractional-Order Delayed Rolling Mill’s Main Drive Electromechanical Coupling System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rui Zhang ◽  
Jinbin Wang ◽  
Lifeng Ma
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Electromechanical Coupling ◽  
System Stability ◽  
Coupling System

This work is focused on a rolling mill’s main drive electromechanical coupling system. Firstly, we equip electromechanical coupling system with fractional-order time delay. Secondly, we, respectively, derive the conditions for occurrence of Hopf bifurcation around equilibriums E 0 0 , 0 , 0 , 0 and E 1 x 1 ∗ , 0 , x 3 ∗ , 0 . It is found that the fractional order α and time delay τ in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.

scholarly journals Double Hopf Bifurcation with Strong Resonances in Delayed Systems with Nonlinerities

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
J. Xu ◽  
K. W. Chung
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Efficient Method ◽  
Cubic Nonlinearity ◽  
Van Der Pol ◽  
Delayed Systems ◽  
Double Hopf Bifurcation ◽  
Codimension Two ◽  
System With Time Delay

An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the 1 : 2 double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity. The results show that 1 : 2 resonance can lead to codimension-three and codimension-two bifurcations. The validity of analytical predictions is shown by their consistency with numerical simulations.

Stability analysis of a nonlinear electromechanical coupling transmission system with time delay feedback

2016 ◽  
Vol 86 (3) ◽  
pp. 1863-1874 ◽  
Author(s):  
Shuang Liu ◽  
Shuangshuang Zhao ◽  
Ben Niu ◽  
Jianxiong Li ◽  
Haibin Li
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Electromechanical Coupling ◽  
Transmission System ◽  
System With Time Delay

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.

FOLD–HOPF BIFURCATION ANALYSIS FOR A COUPLED FITZHUGH–NAGUMO NEURAL SYSTEM WITH TIME DELAY

2010 ◽  
Vol 20 (12) ◽  
pp. 3919-3934 ◽  
Author(s):  
BIN ZHEN ◽  
JIAN XU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Signal Transmission ◽  
Neural System ◽  
Center Manifold Reduction ◽  
Delayed Coupling ◽  
Normal Form Method ◽  
Manifold Reduction ◽  
System With Time Delay

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered. For a critical case when the corresponding characteristic equation has a single zero root and a pair of purely imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. The Fold–Hopf bifurcation diagrams are provided to illustrate the correctness of our theoretical analysis. Whether almost periodic motion and bursting behavior occur in the FHN neural system with delayed coupling depends on the time delay in the signal transmission between the neurons.

Hopf Bifurcation of a Magnetic Bearing System with Time Delay

2004 ◽  
Vol 127 (4) ◽  
pp. 362-369 ◽  
Author(s):  
J. C. Ji ◽  
Colin H. Hansen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Magnetic Bearing ◽  
Complex Conjugate ◽  
Infinite Dimensional ◽  
System With Time Delay ◽  
Two Degree Of Freedom

This paper is concerned with a study of the influence of a time delay occurring in a PD feedback control on the dynamic stability of a rotor suspended by magnetic bearings. In the presence of geometric coordinate coupling and time delay, the equations of motion governing the response of the rotor are a set of two-degree-of-freedom nonlinear differential equations with time delay coupling in nonlinear terms. It is found that as the time delay increases beyond a critical value, the equilibrium position of the rotor motion becomes unstable and may bifurcate into two qualitatively different kinds of periodic motion. The resultant Hopf bifurcation is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. Based on the reduction of the infinite dimensional problem to the flow on a four-dimensional center manifold, the bifurcating periodic solutions are investigated using a perturbation method.

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