Forcing the escape: Partial control of escaping orbits from a transient chaotic region

TL;DR

This paper introduces a novel control algorithm based on partial control methods to predictably force escapes from chaotic transient regions affected by noise, with applications demonstrated in three different cases.

Contribution

It develops a new control algorithm that adapts partial control to intentionally induce escapes, introducing escape functions and sets for straightforward orbit control.

Findings

Successfully controlled escape timing in chaotic systems.

Applied the method to three different case studies.

Demonstrated predictability and robustness of the control algorithm.

Abstract

A new control algorithm based on the partial control method has been developed. The general situation we are considering is an orbit starting in a certain phase space region Q having a chaotic transient behavior affected by noise, so that the orbit will definitely escape from Q in an unpredictable number of iterations. Thus, the goal of the algorithm is to control in a predictable manner when to escape. While partial control has been used as a way to avoid escapes, here we want to adapt it to force the escape in a controlled manner. We have introduced new tools such as escape functions and escape sets that once computed makes the control of the orbit straightforward. We have applied the new idea to three different cases in order to illustrate the various application possibilities of this new algorithm.