Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems

In this paper, we define a simple criterion of the synchronization threshold in the set of coupled chaotic systems (flows or maps) with diagonal diffusive coupling. The condition of chaotic synchronization is determined only by two “parameters of order” i.e., the largest Lyapunov exponent and the coupling coefficient. Our approach can be applied for both regular chaotic networks and arrays or lattices of chaotic oscillators with irregular, arbitrarily assumed structure of coupling. The main idea of the synchronization stability criterion is based on linear analysis of the ensembles of simplest dynamical systems. Numerical simulations confirm that such a linear approach approximates the synchronization threshold with high precision.