Homoclinic motions and chaos in the quasiperiodically forced van der Pol-Duffing oscillator with single well potential

Author:

Abstract

We study a two-frequency quasiperiodically forced oscillator with single well po­tential which reduces to the van der Pol and Duffing oscillators in certain special cases. The unperturbed system without damping and forcing terms has a one-parameter family of periodic orbits. We concentrate on the dynamics near the unperturbed resonant periodic orbits. Using the second-order averaging method and a version of Melnikov’s method, we show that when double resonance occurs, the stable and unstable manifolds of normally hyperbolic invariant tori intersect transversely, i. e. transverse homoclinic motions exist, near the unperturbed reso­nant periodic orbits in certain parameter regions. Such homoclinic motions yield chaotic dynamics characterized by a generalization of the Bernoulli shift. Numer­ical simulation results are also given to demonstrate the theoretical results.

Publisher

The Royal Society

Subject

General Medicine

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