Finite/Fixed-Time Anti-Synchronization of Inconsistent Markovian Quaternion-Valued Memristive Neural Networks With Reaction-Diffusion Terms

In this paper, a novel class of quaternion-valued memristive neural networks (QVMNNs) that considers both the spatial factor and Markov jump phenomenon is proposed, the finite/fixed-time anti-synchronization (F/FTAS) of which is investigated. It is worth mentioning that the considered master and slave systems are assumed to jump along two inconsistent Markov chains, which is a first attempt at the issue of the anti-synchronization of Markovian systems and may be more realistic than most existing Markovian systems' models. Then, a suitable feedback controller is designed, such that the error system can be finite/fixed-time stable. Moreover, by integrating algebraic inequality technologies and Lyapunov theory, a new F/FTAS theorem can be obtained for the proposed systems. Finally, this paper provides two examples, so that the rationality, superiority, and practical value of the main results can be illustrated.