Abstract
Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes van der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-for various resonant cases. Finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.
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Wei, Z., Quan-zhong, H. & Li, L. Heteroclinic orbit and subharmonic bifurcations and chaos of nonlinear oscillator. Appl Math Mech 13, 217–226 (1992). https://doi.org/10.1007/BF02457367
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DOI: https://doi.org/10.1007/BF02457367