Synchronization and anti-synchronization of chaos in an extended Bonhöffer–van der Pol oscillator using active control

2009 ◽  
Vol 319 (1-2) ◽  
pp. 41-49 ◽  
Author(s):  
A.N. Njah ◽  
U.E. Vincent
Keyword(s):  
Active Control ◽  
Van Der Pol Oscillator ◽  
Van Der Pol

DYNAMICS AND ACTIVE CONTROL OF MOTION OF A DRIVEN MULTI-LIMIT-CYCLE VAN DER POL OSCILLATOR

2007 ◽  
Vol 17 (04) ◽  
pp. 1343-1354 ◽  
Author(s):  
R. YAMAPI ◽  
B. R. NANA NBENDJO ◽  
H. G. ENJIEU KADJI
Keyword(s):  
Limit Cycle ◽  
Active Control ◽  
Coupling Parameter ◽  
Van Der Pol Oscillator ◽  
External Excitation ◽  
Van Der Pol ◽  
Chaotic Vibrations ◽  
Van Der Pol Model ◽  
Nonautonomous Case ◽  
Selection Of

This paper deals with the dynamics and active control of a driven multi-limit-cycle Van der Pol oscillator. The amplitude of the oscillatory states both in the autonomous and nonautonomous case are derived. The interaction between the amplitudes of the external excitation and the limit-cycles are also analyzed. The domain of the admissible values on the amplitude for the external excitation is found. The effects of the control parameter on the behavior of a driven multi-limit-cycle Van der Pol model are analyzed and it appears that with the appropriate selection of the coupling parameter, the quenching of chaotic vibrations takes place.

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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