Stabilisation of unstable periodic orbits for chaotic systems with fractal dimension close to an integer

Abstract

In this paper we report the use of an extension of the Ott-Grebogi-Yorke (OGY) approach for controlling chaos, but instead of using a Poincaré Map we use the First Return Map (FRM) of the generated flow. This allows us to deal with systems whose chaotic attractors has a fractal dimension close to an integer value. The method uses only a measurement of one system variable. We take some available parameter as the perturbation parameter, which is changed to force the state trajectory to fall into the stable manifold of the equilibrium point of the FRM.