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- W3111808214 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." @default.
- W3111808214 created "2020-12-21" @default.
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- W3111808214 date "2020-12-09" @default.
- W3111808214 modified "2023-09-27" @default.
- W3111808214 title "Independent Period-2 Motions to Chaos in a van der Pol–Duffing Oscillator" @default.
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- W3111808214 doi "https://doi.org/10.1142/s0218127420300451" @default.
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