Generalized fixed-time synchronization of two different high-order hyperchaotic systems

The main purpose of this paper is to address the problem of fixed-time synchronization for two different higher-order hyperchaotic systems. Therefore, we have given some important lemmas and relied on the basic theories such as the stability theory of Lyapunov and the theory of fixed-time for designing effective fixed-time control laws. The designed control laws to guarantee generalized fixed-time synchronization are different from that in the existing works of the literature. Fixed-time synchronization of two identical chaotic systems has previously been studied, but generalized fixed-time synchronization between two non-identical higher-order hyperchaotic systems is the first of its kind. Among the benefits of the proposed scheme is the simplicity of designed control, in addition to the possibility of achieving synchronization between almost all the various chaotic systems in a short time. To accurately verify the effectiveness of the design scheme and support the theoretical results, two illustrative examples were presented with numerical simulation. One of the two examples was suggested to study the synchronization between two different chaotic systems, while the second example was applied between two sixth-dimensional hyperchaotic systems.