Tracking inherent periodic orbits in chaotic system via adaptive time delayed self-control

Abstract

An adaptive time delayed self-control for tracking inherent periodic orbits in chaotic systems is studied. It is shown that by using the gradient descent based search algorithm, the time delay constant can be tuned towards any period of inherent periodic orbits. Under the proposed control strategy, analytic or numerical solutions of the inherent periodic orbits, which are difficult to derive but absolutely necessary for tracking using conventional control strategies, are not necessary. Simulation results are presented to show the effectiveness of the approach.