This paper studies the existence of Hlder continuity of bidirectionally coupled generalised synchronisation (GS).Based on the slaving principle of synergetics and the modified system approach,it classifies the GS into several types.The existences of two main types of Holder continuous bidirectionally coupled GS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem.Numerical simulations illustrate the theoretical results.
A complex network consisting of chaotic systems is considered and the existence of the Hlder 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.
The impulsive synchronization problem of two identical chaotic ratchets is investigated in this paper. We demon-strate that the impulsive method to control directed transport is applicable when there are multiple co-existing attrac-tors in phase space transporting particles in different directions. Numerical simulations are carried out to illustrate the effectiveness of the proposed method.
