Strange attractors and chaos control in a Duffing–Van der Pol oscillator with two external periodic forces

2004 ◽  
Vol 277 (4-5) ◽  
pp. 783-799 ◽  
Author(s):  
F.M. Moukam Kakmeni ◽  
S. Bowong ◽  
C. Tchawoua ◽  
E. Kaptouom
Keyword(s):  
Chaos Control ◽  
Strange Attractors ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

Chaos control and synchronization of a Φ6-Van der Pol oscillator

2004 ◽  
Vol 322 (5-6) ◽  
pp. 305-323 ◽  
Author(s):  
F.M Moukam Kakmeni ◽  
Samuel Bowong ◽  
Clement Tchawoua ◽  
Ernest Kaptouom
Keyword(s):  
Chaos Control ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Control And Synchronization

Period-doubling cascades and strange attractors in the triple-well φ6-Van der Pol oscillator

2008 ◽  
Vol 78 (2) ◽  
pp. 025003 ◽  
Author(s):  
Jun Yu ◽  
Rongbo Zhang ◽  
Weizhen Pan ◽  
L Schimansky-Geier
Keyword(s):  
Period Doubling ◽  
Strange Attractors ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

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.

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