Bipartite synchronization of competition-cooperation neural networks and its application via truncated sampled-data control.

This paper proposes a scheme to reduce coupling strength and achieve bipartite synchronization in competition-cooperation neural networks based on truncated sampled-data control. In this approach, the truncated sampled-data control means that only partial sampling information is used and the rest are discarded. Based on this, this paper proposes the concept of maximum data truncation rate, which quantitatively characterizes the bandwidth savings. A pinning truncated sampled-data controller associated with competition-cooperation interactions is designed, and a tractable error system is constructed using coordinate transformation techniques. Then, aiming at reducing coupling strength, a dual-interval-dependent Lyapunov function is designed according to the characteristics of the control scheme and the network structure. Combining Lyapunov theory with inequality techniques, two sufficient criteria are developed to ensure the bipartite synchronization of competition-cooperation neural networks. Based on these criteria, two algorithms are developed to determine the minimum allowable coupling strength and the maximum allowable data truncation rate, respectively. Two improvements over the previous Lyapunov functions are discussed: reducing the allowable coupling strength and increasing the allowable data truncation rate. Finally, the advantages and effectiveness of the proposed control scheme are demonstrated by an application and numerical examples.