Partial synchronization on a network with different classes of oscillators

Abstract

Complete and partial synchronization have been largely studied on networks of identical coupled oscillators. However, we study a network in which not all oscillators when uncoupled show the same dynamics and nonetheless the network shows partial synchronization. Our system is composed by four Rössler oscillators diffusively coupled in a ring. Oscillators 1 and 3 are identical, as 2 and 4 are also. In short, the network is said to be composed of different classes of oscillators in our example, two classes with two oscillators each . Primary synchronization is defined as the case when all oscillators on the same class are identically synchronized, for all classes. Secondary synchronization is related to the other possible cases of partial synchronization. Both are achieved for the system we have chosen, shown by means of direct integration and transverse Lyapunov exponent computation. Furthermore, evidence of riddled basins of attraction is presented.