A Novel Coupled Memristive Izhikevich Neuron Model and Its Complex Dynamics

Abstract

This paper proposes a novel, five-dimensional memristor synapse-coupled Izhikevich neuron model under electromagnetic induction. Firstly, we analyze the global exponential stability of the presented system by constructing an appropriate Lyapunov function. Furthermore, the Hamilton energy functions of the model and its corresponding error system are derived by using Helmholtz’s theorem. In addition, the influence of external current and system parameters on the dynamical behavior are investigated. The numerical simulation results indicate that the discharge pattern of excitatory and inhibitory neurons changes significantly when the amplitude and frequency of the external stimulus current are applied at different degrees. And the crucial dynamical behavior of the neuronal system is determined by the intensity of modulation of the induced current and the gain in the electromagnetic induction. Moreover, the amount of Hamilton energy released by the model could be evaluated during the conversion between the distinct dynamical behaviors.