TARGETING AND CONTROL OF SYNCHRONIZATION IN CHAOTIC OSCILLATORS

Abstract

A method of targeting synchronization and its control is reported in chaotic oscillators. A design of appropriate coupling is proposed using an open-plus-closed-loop (OPCL) scheme based on Hurwitz stability to realize a desired state of synchrony between the oscillators. A general theory of the coupling definition is described for unidirectional as well as bidirectional mode. In a synchronization state, a chaotic attractor can be scaled up or down in size relative to another attractor. Additionally, a technique of controlling synchronization is introduced that allows a smooth transition from complete synchronization to antisynchronization or vice versa, by varying a parameter inserted in the coupling definition without loss of stability during the transition. A smooth scaling of the size of the attractor is also implemented. Numerical examples are given using a Sprott system. Physical realization of the OPCL coupling under bidirectional mode and control of synchronization under unidirectional mode is demonstrated in an electronic circuit.