Spatial patterns and chimera states in discrete memristor coupled neural networks

Memristors have good plasticity, and they have been used to simulate the synaptic structure and reproduce the dynamics of biological neurons. Recently, the discrete memristor neural networks have become a research hotspot. In this paper, the dynamics of the Rulkov neuron model are investigated by bifurcation diagrams, Lyapunov exponents, and firing modes analysis. Then neural networks are constructed by discrete memristor coupling, and different firing cases are discussed respectively. The phase synchronization is analyzed between two neurons coupled by a discrete memristor. The chimera states are studied in a discrete memristor ring neural network. In addition, the target waves and spiral waves are generated in a discrete memristor lattice neural network. Simulation results show that the discrete memristor plays a good role as a synapse. It controls the synchronous behaviors of networks, and displays the same spatial patterns of biological neurons in the networks. These results throw light on the construction of artificial networks and neuromorphic architectures.