Conclusions
In this paper, we have studied the bipartite leader-following synchronization in a network of delayed neural networks under signed graph based on pinning control strategy, where only a subset of nodes can access the information of the leader. By using the property of M-matrix and the theory of algebraic graphs, we have established some conditions to ensure that the bipartite leader-following synchronization problem of the signed network can be successfully solved. Both differentiable and non-differentiable cases for the node-delay in the network have been considered by using some techniques from delayed systems such as Jensen’s inequality and the reciprocally convex approach. Moreover, when the node-delay is bounded and differentiable, a simple algebraic approach is given to estimate an upper bound of the node-delay. Simulation results have been provided to validate the effectiveness of our theoretical analysis. It is worth mentioning that the bipartite leaderless synchronization of the signed network has also been briefly discussed. For the coupled delayed neural networks in this paper, the signed interaction graph is assumed to be fixed and the communication delay between neighboring nodes has not been considered. It would be of interest to investigate the bipartite synchronization of coupled delayed neural networks with switching network topology and hybrid delayed coupling in the near future.
