Coopetition-dependent controller design for bipartite synchronization of cooperation-competition delayed memristive neural networks

In this paper, the bipartite synchronization problem for cooperation-competition delayed memristive neural networks (CCDMNNs) is addressed via designing a coopetition-dependent controller. Based on the coordinate transformation technique, an easy-to-analyze error system is constructed in the presence of cooperation-competition interactions. Two control strategies are proposed respectively to realize bipartite synchronization. First of all, a coopetition-dependent controller that can eliminate the impact of cooperation-competition interactions as well as the time-varying state-dependent memristive connection weights is designed. In combination with inequality techniques, the Lyapunov theory and the interval matrix method, an LMI-form criterion is established to ensure the bipartite synchronization of CCDMNNs. Moreover, an adaptive controller that can automatically adjusts the control parameters to achieve appropriate control gains is proposed to further improve the control performance. Finally, a numerical example is given to verify the correctness and superiority of the proposed control schemes.