Hölder continuity of generalized chaos synchronization in complex networks

A complex network consisting of chaotic systems is considered and the existence of the Hölder continuous generalized synchronization in the network is studied. First, we divide nodes of the network into two parts according to their dynamical behaviour. Then, based on the Schauder fixed point theorem, sufficient conditions for the existence of the generalized synchronization between them are derived. Moreover, the results are theoretically proved. Numerical simulations validate the theory.