Bursts in the Chaotic Trajectory Lifetimes Preceding the Controlled Periodic Motion

Abstract

The average lifetime ($\tau (H)$) it takes for a randomly started trajectory to land in a small region ($H$) on a chaotic attractor is studied. $\tau (H)$ is an important issue for controlling chaos. We point out that if the region $H$ is visited by a short periodic orbit, the lifetime $\tau (H)$ strongly deviates from the inverse of the naturally invariant measure contained within that region (${\mu }_N(H{)}^{-1}$). We introduce the formula that relates $\tau (H)/{\mu }_N(H{)}^{-1}$ to the expanding eigenvalue of the short periodic orbit visiting $H$.

Accepted for publication in Phys. Rev. E, 3 PS figures

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