Hölder continuity of two types of generalized synchronization manifold.

This paper studies the existence of Hölder continuity of generalized synchronization (GS). Based on the modified system approach, GS is classified into three types: equilibrium GS, periodic GS, and C-GS, when the modified system has an asymptotically stable equilibrium, asymptotically stable limit cycles, and chaotic attractors, respectively. The existence of the first two types of Hölder continuous GS inertial manifolds are strictly theoretically proved.