Bipartite synchronization for coupled memristive neural networks: Memory-based dynamic updating law.

In this paper, bipartite synchronization for memristive neural networks with multi-delay couplings is investigated. The evaluation index of unbounded coupling delays on synchronization could be quantitatively analyzed by considering proportional delay, which will undoubtedly and strongly impede synchronous behavior. By simultaneously taking synchronization and anti-synchronization patterns into account, a novel impulsive controller with a signed form is elaborately designed. For the purpose of selecting suitable impulsive instants, a dynamic self-triggered mechanism is introduced. Additionally, to mitigate the possible risk of the dynamic mechanism transitioning into a static mechanism in exceptional scenarios, a memory-based adaptive updating law is therefore proposed in this paper. It should be noted that the adaptive control related dynamic parameters considered in this paper are in a non-monotonic form. By utilizing Lyapunov stability theorem, parameter variation approach and contradiction analysis method, sufficient conditions for ensuring the synchronization are successfully derived. Finally, two experiments are presented to demonstrate the practicability of the derived results. • Synchronization patterns and anti-synchronization patterns in some previous works could be thought as one of the special cases in our paper. • A non-monotonic dynamic updating law is devised by incorporating memory information, specifically utilizing the sparse historical states of nodes. • Lower bound of dynamic parameter is proved to be greater than a specific positive scalar in this work, that is, the importance of the role played by the dynamic parameter in determining impulsive intervals is enhanced. [ABSTRACT FROM AUTHOR]