An analytic criterion for generalized synchronization in unidirectionally coupled systems based on the auxiliary system approach

An analytic criterion is developed to investigate generalized synchronization (GS) in unidirectionally coupled systems based on the auxiliary system approach. The criterion is derived by transforming the existence problem of generalized synchronization into an eigenvalue problem. Numerical simulations show that the analytic criterion is almost as accurate as the response Lyapunov exponents method, and may provide an estimation of the threshold of strong generalized synchronization. A significant result can be deduced from our analysis that the more the number of equilibria of the unidirectionally coupled systems, the greater the chance of generalized synchronization, but the harder it may be for strong generalized synchronization to occur.