Hölder continuity of generalized synchronization of three bidirectionally coupled chaotic systems

This Letter studies the existence of Hölder continuity of generalized synchronization (GS). The model considered here includes three bidirectionally coupled chaotic systems, two of them denote the driving systems, while the other stands for the response system. Based on the modified system approach, GS is classified into several types, and two kinds therein are investigated. By using the Schauder fixed point theorem, sufficient conditions for the existence of Hölder continuous GS are derived and theoretically proved. In addition, numerical examples are given for verification.