Dynamics of a multiplex neural network with delayed couplings

Abstract

Multiplex networks have drawn much attention since they have been observed in many systems, e.g., brain, transport, and social relationships. In this paper, the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied. The stability and bifurcation of the network equilibrium are discussed, and interesting neural activities of the network are explored. Based on the neuron circuit, transfer function circuit, and time delay circuit, a circuit platform of the network is constructed. It is shown that delayed couplings play crucial roles in the network dynamics, e.g., the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence.

The PDP feedback control design and exponential stability for a star-shaped network of open channels

“…A systematic approach for stabilizing a class of linear undamped systems of multiple degrees of freedom with PDP feedbacks is presented in Liu and Hu. 30 The nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied in Mao et al, 31 which shows that the delayed couplings play crucial roles in the network dynamics, for example, the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence. The sufficient and necessary conditions of delay-independent exponential stability for a delayed ring neuron network is presented in Zhao and Wang.…”