On the dynamics of a time-periodic equation

Abstract

In this paper we use the second order equation $\frac{d^{2}q}{d{t}^2}+(\lambda -\gamma q^2)\frac{dq}{dt}-q+q^3=\mu q^2\sin \omega t$ as a demonstrative example to illustrate how to apply the analysis of \cite{WO} and \cite{WOk} to the studies of concrete equations. We prove, among many other things, that there are positive measure sets of parameters $(\lambda ,\gamma ,\mu ,\omega )$ corresponding to the case of intersected and the case of separated stable and unstable manifold of the solution $q(t)=0$, $t\in \mathbb{R}$ respectively, so that the corresponding equations admit strange attractors with SRB measures.

References in corpus (1)

• Dissipative homoclinic loops and rank one chaos