Targeting and Control of Synchronization in Chaotic oscillators

A method of targeting synchronization and its control is reported in chaotic oscillators. This proposes design of appropriate coupling using an open-plus-closed-loop (OPCL) scheme based on Hurwitz stability to establish a desired state of synchrony between the oscillators. In the 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 tuning a system parameter without loss of stability. A smooth scaling of the size of the attractor is also implemented. The general theory of the coupling definition is described for unidirectional as well as bidirectional mode. Numerical examples are given using a Sprott system. Physical realization of the OPCL coupling and control of synchronization is demonstrated in electronic circuit. Index-Synchronization, chaotic oscillator, coupling design, Sprott circuit.