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- Title
Independent Period-2 Motions to Chaos in a van der Pol–Duffing Oscillator.
- Authors
Xu, Yeyin; Luo, Albert C. J.
- Abstract
In this paper, an independent bifurcation tree of period-2 motions to chaos coexisting with period-1 motions in a periodically driven van der Pol–Duffing oscillator is presented semi-analytically. Symmetric and asymmetric period-1 motions without period-doubling are obtained first, and a bifurcation tree of independent period-2 to period-8 motions is presented. The bifurcations and stability of the corresponding periodic motions on the bifurcation tree are determined through eigenvalue analysis. The symmetry breaks of symmetric period-1 motions is determined by the saddle-node bifurcations, and the appearance of the independent bifurcation tree of period-2 motions to chaos is also due to the saddle-node bifurcations. Period-doubling cascaded scenario of period-2 to period-8 motions are predicted analytically, and unstable periodic motions are also obtained. Numerical simulations are performed to illustrate motion complexity in such a van der Pol–Duffing oscillator. Such nonlinear systems can be applied in nonlinear circuit design and fluid-induced oscillations.
- Subjects
DUFFING equations; PERIODIC motion; MOTION; SYMMETRY breaking; VAN der Pol oscillators (Physics); NONLINEAR systems; DOUBLE walled carbon nanotubes; NONLINEAR oscillators
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2020, Vol 30, Issue 15, pN.PAG
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127420300451