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

scholarly journals New periodic-chaotic attractors in slow-fast Duffing system with periodic parametric excitation

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Xianghong Li ◽  
Yongjun Shen ◽  
Jian-Qiao Sun ◽  
Shaopu Yang
Keyword(s):  
Parametric Excitation ◽  
Chaotic Attractors ◽  
Duffing System

Three Conditions Lyapunov Exponents Should Satisfy

2003 ◽  
Author(s):  
Jingjun Lou ◽  
Shijian Zhu
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic Motion ◽  
The Other ◽  
Cubic Nonlinearity ◽  
3 Dimensional ◽  
Duffing System ◽  
Dissipative Dynamical System

In contrast to the unilateral claim in some papers that a positive Lyapunov exponent means chaos, it was claimed in this paper that this is just one of the three conditions that Lyapunov exponent should satisfy in a dissipative dynamical system when the chaotic motion appears. The other two conditions, any continuous dynamical system without a fixed point has at least one zero exponent, and any dissipative dynamical system has at least one negative exponent and the sum of all of the 1-dimensional Lyapunov exponents id negative, are also discussed. In order to verify the conclusion, a MATLAB scheme was developed for the computation of the 1-dimensional and 3-dimensional Lyapunov exponents of the Duffing system with square and cubic nonlinearity.

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
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