Bipartite secure synchronization criteria for coupled quaternion-valued neural networks with signed graph.

This study explores the bipartite secure synchronization problem of coupled quaternion-valued neural networks (QVNNs), in which variable sampled communications and random deception attacks are considered. Firstly, by employing the signed graph theory, the mathematical model of coupled QVNNs with structurally-balanced cooperative-competitive interactions is established. Secondly, by adopting non-decomposition method and constructing a suitable unitary Lyapunov functional, the bipartite secure synchronization (BSS) criteria for coupled QVNNs are obtained in the form of quaternion-valued LMIs. It is essential to mention that the structurally-balanced topology is relatively strong, hence, the coupled QVNNs with structurally-unbalanced graph are further studied. The structurally-unbalanced graph is treated as an interruption of the structurally-balanced graph, the bipartite secure quasi-synchronization (BSQS) criteria for coupled QVNNs with structurally-unbalanced graph are derived. Finally, two simulations are given to illustrate the feasibility of the suggested BSS and BSQS approaches.