Neimark bifurcation, almost-periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance

Physics Letters A ◽

10.1016/0375-9601(94)90244-5 ◽

1994 ◽

Vol 192 (2-4) ◽

pp. 201-206 ◽

Author(s):

Wanda Szemplińska-Stupnicka ◽

Jerzy Rudowski

Keyword(s):

Almost Periodicity ◽

Principal Resonance ◽

Van Der Pol ◽

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Dynamical Response of a Van der Pol–Duffing System with an External Harmonic Excitation and Fractional Derivative

Springer Proceedings in Mathematics & Statistics - Applied Non-Linear Dynamical Systems ◽

10.1007/978-3-319-08266-0_10 ◽

2014 ◽

pp. 139-150

Author(s):

Arkadiusz Syta ◽

Grzegorz Litak

Keyword(s):

Fractional Derivative ◽

Harmonic Excitation ◽

Dynamical Response ◽

Van Der Pol ◽

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

Journal of Sound and Vibration ◽

10.1016/j.jsv.2007.05.027 ◽

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 ◽

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

Nonlinear Dynamics ◽

10.1007/s11071-007-9238-x ◽

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 ◽

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Global robust synchronization of the Duffing system and Van der Pol oscillator

2008 47th IEEE Conference on Decision and Control ◽

10.1109/cdc.2008.4738667 ◽

2008 ◽

Author(s):

Weijie Sun ◽

Daizhan Cheng ◽

Jie Huang

Keyword(s):

Van Der Pol Oscillator ◽

Van Der Pol ◽

Duffing System ◽

Robust Synchronization

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

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.110967 ◽

2021 ◽

Vol 147 ◽

pp. 110967

Author(s):

Xindong Ma ◽

Daixian Xia ◽

Wenan Jiang ◽

Mao Liu ◽

Qinsheng Bi

Keyword(s):

Van Der Pol ◽

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

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns.2005.6.1.63 ◽

2005 ◽

Vol 6 (1) ◽

Author(s):

Yanyan Zhang ◽

Jian Xu

Keyword(s):

Hopf Bifurcations ◽

Van Der Pol ◽

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Quantization and classical limit of a linearly damped particle, a van der Pol System and a Duffing System

Random Operators and Stochastic Equations ◽

10.1515/rose.2001.9.3.275 ◽

2001 ◽

Vol 9 (3) ◽

Author(s):

A. O. BOLIVAR

Keyword(s):

Classical Limit ◽

Van Der Pol ◽

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Pragmatical adaptive chaos control from a new double van der Pol system to a new double Duffing system

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.05.011 ◽

2008 ◽

Vol 203 (2) ◽

pp. 513-522 ◽

Author(s):

Zheng-Ming Ge ◽

Shih-Chung Li ◽

Shih-Yu Li ◽

Ching-Ming Chang

Keyword(s):

Chaos Control ◽

Van Der Pol ◽

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Analysis and Controlling of Hopf Bifurcation for Chaotic Van Der Pol-Duffing System

Mathematical and Computational Applications ◽

10.3390/mca19030184 ◽

2014 ◽

Vol 19 (3) ◽

pp. 184-193 ◽

Author(s):

Ping Cai ◽

Jia-Shi Tang ◽

Zhen-Bo Li

Keyword(s):

Hopf Bifurcation ◽

Van Der Pol ◽

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Chaos synchronization of a fractional-order modified Van der Pol-Duffing system via new linear control, backstepping control and Takagi-Sugeno fuzzy approaches

10.1002/cplx.21719 ◽

2015 ◽

Vol 21 (S1) ◽

pp. 116-124 ◽

Author(s):

Ahmed Ezzat Matouk

Keyword(s):

Fractional Order ◽

Chaos Synchronization ◽

Backstepping Control ◽

Linear Control ◽

Van Der Pol ◽

Duffing System ◽

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