The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

The existence of two types of generalized synchronisation is studied. The model considered here includes three bidirectionally coupled chaotic systems, and two of them denote the driving systems, while the rest stands for the response system. Under certain conditions, the existence of generalised synchronisation can be turned to a problem of compression fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalised synchronisation manifold. Numerical simulations validate the theory.