Effect of bounded noise on the chaotic motion of a Duffing Van der pol oscillator in a ϕ6 potential

2006 ◽  
Vol 27 (3) ◽  
pp. 778-788 ◽  
Author(s):  
Xiaoli Yang ◽  
Wei Xu ◽  
Zhongkui Sun
Keyword(s):  
Chaotic Motion ◽  
Van Der Pol Oscillator ◽  
Bounded Noise ◽  
Van Der Pol

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

Investigation on Dynamics of the Extended Duffing-Van der Pol System

2009 ◽  
Vol 64 (5-6) ◽  
pp. 341-346 ◽  
Author(s):  
Jun Yu ◽  
Jieru Li
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Nonlinear System ◽  
Computer Simulations ◽  
Chaotic Motion ◽  
Dynamical Behaviour ◽  
Higher Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Melnikov Analysis

Abstract The chaotic motion in periodic self-excited oscillators has been extensively investigated through experiments and computer simulations. However, with the advent of the study of chaotic motion by means of strange attractors, Poincar´e map, fractal dimension, it has become necessary to seek for a better understanding of nonlinear system with higher order nonlinear terms. In this paper we consider an extended Duffing-Van der Pol oscillator by introducing a nonlinear quintic term. The dynamical behaviour of the system is investigated by using Melnikov analysis and numerical simulation. The results can help one to understand the essence of given nonlinear system.

NUMERICAL SOLUTION FOR DUFFING-VAN DER POL OSCILLATOR VIA BLOCK METHOD

2020 ◽  
Vol 10 (1) ◽  
pp. 1857-8365
Author(s):  
A. F. Nurullah ◽  
M. Hassan ◽  
T. J. Wong ◽  
L. F. Koo
Keyword(s):  
Numerical Solution ◽  
Van Der Pol Oscillator ◽  
Block Method ◽  
Van Der Pol

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

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