Hölder continuity of two types of bidirectionally coupled generalised synchronisation manifold

This paper studies the existence of Höolder 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 Hölder continuous bidirectionally coupled GS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.