Classification and Computation of Non-resonant Double Hopf Bifurcations and Solutions in Delayed van der Pol-Duffing System

2005 ◽  
Vol 6 (1) ◽  
Author(s):  
Yanyan Zhang ◽  
Jian Xu
Keyword(s):  
Hopf Bifurcations ◽  
Van Der Pol ◽  
Duffing System

Chaotic motion of Van der Pol–Mathieu–Duffing system under bounded noise parametric excitation

2008 ◽  
Vol 309 (1-2) ◽  
pp. 330-337 ◽  
Author(s):  
Jiaorui Li ◽  
Wei Xu ◽  
Xiaoli Yang ◽  
Zhongkui Sun
Keyword(s):  
Parametric Excitation ◽  
Chaotic Motion ◽  
Bounded Noise ◽  
Van Der Pol ◽  
Duffing System

Frequency locking in a forced Mathieu–van der Pol–Duffing system

2007 ◽  
Vol 54 (1-2) ◽  
pp. 3-12 ◽  
Author(s):  
Manoj Pandey ◽  
Richard H. Rand ◽  
Alan T. Zehnder
Keyword(s):  
Frequency Locking ◽  
Van Der Pol ◽  
Duffing System

scholarly journals Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Stochastic System ◽  
Critical Parameter ◽  
Random Parameter ◽  
Order System ◽  
Hopf Bifurcations ◽  
Van Der Pol ◽  
Existence Conditions ◽  
Theoretical Results

The Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.

Compound bursting behaviors in a forced Mathieu-van der Pol-Duffing system

2021 ◽  
Vol 147 ◽  
pp. 110967
Author(s):  
Xindong Ma ◽  
Daixian Xia ◽  
Wenan Jiang ◽  
Mao Liu ◽  
Qinsheng Bi
Keyword(s):  
Van Der Pol ◽  
Duffing System
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