Synchronous dynamics in neural system coupled with memristive synapse

To study the collective behavior and the regulation mechanism of memristor, the Hindmarsh-Rose neuron cells are selected as the units to construct a coupled system by using the cubic flux-controlled memristor as a connecting synapses, both the firing mode and synchronous behavior in this coupled system are investigated. In this paper, a coefficient is introduced to describe the effect of electromagnetic induction of membrane potential, and the weights of synaptic connection between cells are selected as an adjustable parameter. We have found that, on the one hand, for the certain external current, the firing pattern of neurons could maintain normal state induced by proper electromagnetic induction, and the transition between different firing states could also be observed. On the other hand, both the synchronous effects could be effectively enhanced and the domain of synchronous parameters could be also expanded by tuning the electromagnetic parameters. Particularly, when the coupled system is in the synchronization state, one can see that the firing behavior of neurons will simultaneously change with the varying of the memristance. The similar phenomenon could also be found by introducing the external stimulus signal with a certain frequency. It means that the plasticity of biological synapses could be effectively mimicked by using the memristive synapse and thus the effective memory function of the memristor to the external stimulus signal may be realized. Above results may not only provide some useful clues for understanding the dynamic behavior of neural system coupled with memristive synapses, but also afford us some inspiration to simulate human brain memory, forgetting or some other functions by using the memristor neural network in the future.