Targetability of chaotic sets with small parameter perturbations

TL;DR

This paper demonstrates that small parameter perturbations can effectively steer orbits into neighborhoods of chaotic sets, leveraging geometric control theory and Lie rank conditions.

Contribution

It establishes a method to target chaotic sets using minimal parameter adjustments based on geometric control theory.

Findings

Small parameter perturbations can steer orbits into chaotic neighborhoods.

Lie rank condition is sufficient for targetability.

The approach applies to systems satisfying geometric control criteria.

Abstract

In this paper targetability of chaotic sets with small controls is discussed by virtue of some results of geometric control theory. It is proved that given a chaotic set {\Lambda}, it is possible to steer a orbit in to every final state in some neighborhood of the chaotic set by suitable small perturbations to the parameters of the system under the Lie rank condition.