Synchronous Dynamics in Multilayer Memristive Neural Networks: Effect of Electromagnetic Induction

Abstract

Brain has a hierarchical structure with multiple connection types. To further explore the effect of electromagnetic induction on biological neural networks, in this paper, a two-layer small-world neuronal network with electrical intra-layer connections and memristive inter-layer connections was constructed. In specially, the two layer have different spiking and bursting activities. Electrical coupling strength and electromagnetic induction coefficient are taken as control parameter. Numerical results indicate that the two-layer neurons in different discharge states can achieve synchronization and the firing patterns of the synchronized neurons are related to the electromagnetic induction. Moreover, some particular dynamical states including chimera state and bursting transition are observed in the network. Then, the mechanisms of the two burst transitions are clarified. In addition, the statistical synchronization factor and average error are introduced to measure the intra-layer and inter-layer synchronization, respectively, which reveal that electrical coupling induces and enhances the synchronization more effectively for a higher electromagnetic induction coefficient. Our obtained results indicate that the electromagnetic induction exerts significant impact in modulating the dynamic behavior of neural networks, and provide a useful guidance on the study of physiological functions related to synchronization in the brain.