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.
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献