SUPPRESSION OF CHAOS THROUGH CHANGES IN THE SYSTEM VARIABLES - TRANSIENT CHAOS AND CRISES

In this work a recently introduced chaos suppression method [M.A. Matias and J. Guemez, Phys. Rev. Lett. 72 (1994) 1455-8] is applied to the two-dimensional maps due to Henon and Holmes, respectively, at parameter values for which the system exhibits a non-attracting chaotic set. First of all, it is shown how within a periodic window it is possible to stabilize periodic behaviour with a different periodicity. In addition, for systems that have suffered a crisis it is shown how a chaotic transient can be converted into a strange attractor, namely by switching back to the precrisis behaviour.