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.

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

“…The system does not strictly follow the transition from phase synchronization to perfect synchronization; perfect synchronization occurs before phase synchronization. In [21], for an integer-order model, the synchronization degree is strengthened with increasing 1 k , but in this paper, an exception can be found when the fractional-order is in the range   0.59, 0.64 .…”

“…Content may change prior to final publication. In this paper, from the integer-order memristive synapsecoupled neuronal network proposed in [21] and the fractional-order HR model proposed in [28], the memristive synapse-coupled fractional-order neuronal network constructed by two neurons can be described as follows:…”

“…is introduced in this model [17,18,21,31,32]. Here, A ring network is constructed by some subnetworks that are the abovementioned memristor synapse-coupled networks, and the ring networks involve N subnetworks.…”

“…Memristive synapse-coupling can extend the chaotic synchronization range. Compared with [21], the integer-order coupled neurons are in chaotic synchronization only when the external stimulation current 3 I = , but the fractional-order coupled neurons can be in periodic synchronization when the fractional-order lies within   0.55, 0.73 .…”

“…Memristors controlled by magnetic fluxes can be treated as coupled synapses between neuronal cells. Some studies investigated the chaos and period of a Hopfield network coupled with memristive synapses [18,19] and the rich dynamic behaviors of memristive synapse-coupled neuronal networks [20][21][22]. By adjusting the relevant parameters, different firing models arise, increasing the synchronization efficiency in a memristive synapse-coupled neuronal network [20].…”