Synchronization in Finite/Fixed Time for Markovian Complex-Valued Nonlinear Interconnected Neural Networks with Reaction-Diffusion Terms

This paper considers a novel class of nonlinear interconnected neural networks (INNs) where the Markovian jump parameters and reaction-diffusion terms are both involved. The nonlinear INNs are studied in the complex domain, which is a meaningful attempt in the research on INNs. Then, by designing a suitable nonlinear controller and employing the Lyapunov functional and algebraic inequality technologies, a finite/fixed-time synchronization criterion in probability can be obtained for the $N$ subsystems. Note that the criteria for synchronization in finite time and fixed time are obtained with only one controller and integrated into a unified theorem. A secret communication example is presented, such that the validity and practicability of this paper can be verified.