Design of coupling for synchronization of chaotic oscillators

A general procedure is discussed to formulate a coupling function capable of targeting desired responses such as synchronization, antisynchronization, and amplitude death in identical as well as mismatched chaotic oscillators. The coupling function is derived for unidirectional, mutual, and matrix type coupling. The matrix coupling, particularly, is able to induce synchronization, antisynchronization, and amplitude death simultaneously in different state variables of a response system. The applicability of the coupling is demonstrated in spiking-bursting Hindmarsh-Rose neuron model, Rossler oscillator, Lorenz system, Sprott system, and a double scroll system. We also report a scaling law that defines a process of transition to synchronization.