Experimental Implementation of Migrations in Multiple-attractor Systems

It was shown by Jackson and Grosu [1995a] that entrainment control of a complex dynamic system could be achieved by using an open-plus-closed-loop (OPCL) control action. Jackson [1995] showed that, for multiple-attractor systems, it is also possible to transfer the dynamics of a system between arbitrary attractors, using this control only for a limited period of time (“migration control”). In the case of the Chua system [1986], Jackson and Grosu [1995b] showed that this migration action can be achieved using only a limited pre-recorded signal of one variable of the “target” attractor. Here we study the experimental implementation of this migration action on a Chua circuit with five attractors (fixed points, a limit cycle, and chaotic attractors) [Wu & Pivka, 1994]. It is shown that reliable migrations are possible with a pre-recorded signal of one target variable, provided that the signal is longer than a minimal time, dependent on an adjustable control strength. The minimal time for successful migration is studied for all distinct migration processes. It is also shown that this action is robust to the limited accuracy of the recorded data.