Occasional linear connection for synchronization of chaos

Abstract

This paper considers synchronization of chaos from a simple piecewise linear continuous-time circuit. The chaotic circuit includes a bipolar hysteresis element whose thresholds vary periodically and we can prove observable chaos generation by using one-dimensional return map. Then we propose the occasional linear connection method (ab. OLC) that can realize three kinds of master-slave synchronous states of chaos (in-phase, lagging-phase, and leading-phase synchronous states) and in-phase mutual synchronization of chaos. The OLC is a novel nonlinear method that connects chaos generators by using periodically sampled error, only if the objective states are trapped into some linear region. Then we have given a theoretical evidence for the OLC function. Moreover, we propose a simple implementation example of the OLC and demonstrate its basic performance.