Paper Info
Title
Bifurcations And Chaos Of Duffing-Van Der Pol Equation With Nonsymmetric Nonlinear Restoring And Two External Forcing Terms
Abstract
Bifurcations and chaos of Duffing-van der Pol equation with nonsymmetric nonlinear restoring and two external forcing terms are investigated. The threshold values of the existence of chaotic motion are obtained under periodic perturbation. By the second-order averaging method, we prove the criteria of the existence of chaos in an averaged system under quasi-periodic perturbation for omega(2) = n omega(1) + epsilon sigma, n = 1, 2, 3, 5, and cannot prove the criterion of existence of chaos in an averaged system under quasi-periodic perturbation for omega(2) = n omega(1) + epsilon sigma, n = 4, 6, 7, ... , where sigma is not rational to omega(1), but can show the occurrence of chaos in the original system by numerical simulation. Numerical simulation including homoclinic or heteroclinic bifurcation surfaces, bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare maps, not only show the consistence with the theoretical analysis but also exhibit more new complex dynamical behaviors. We show that cascades of interlocking period-doubling and reverse period-doubling bifurcations lead to interleaving occurrence of chaotic behaviors and quasi-periodic orbits, symmetry-breaking of periodic orbits in chaotic regions, onset of chaos occurring more than once, chaos suddenly disappearing to periodic orbits, strange nonchaotic attractor, nonattracting chaotic set and nice chaotic attractors.
Year
DOI
Venue
2014
10.1142/S0218127414300110
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Duffing-van der Pol equation, Melnikov methods, second averaged methods, bifurcation, chaos
Journal
24
Issue
ISSN
Citations 
3
0218-1274
0
PageRank 
References 
Authors
0.34
1
3
Name
Order
Citations
PageRank
Zhiyan Yang1113.14
Tao Jiang221144.26
Zhujun Jing3348.28