Successive lag synchronization of heterogeneous distributed-order coupled neural networks with unbounded delayed coupling

The problem of successive lag synchronization (SLS) for heterogeneous distributed-order coupled neural networks (HDOCNNs) with unbounded delayed coupling is investigated in this paper. Firstly, a model for HDOCNNs under the framework of distributed order Caputo derivative is proposed which is the generalization of integer order and fractional order cases. Secondly, a new Razumikhin-type stability theorem for distributed order systems is proposed. On this basis, the well-known Halanay type inequality is generalized to analyze the convergence of solutions for a class of distributed order dynamical systems. Thirdly, the SLS criteria for HDOCNNs with delayed coupling by designing a novel adaptive controller and a valid feedback controller are presented herein, respectively. Finally, a numerical example is presented to illustrate the reliability of the proposed scheme.