Dynamical analysis of the FitzHugh–Nagumo model with memristive synapse

Abstract

Understanding the transition mechanism between different activity patterns in realistic neuron models brings forward fundamental challenges for the dynamical systems theory. The knowledge about the mechanisms can present precious predictions and intuitions for determining fundamental principles of neuron functioning. This paper aims to present a dynamic analysis of the FitzHugh–Nagumo neuron model with a memristive synapse. In this article, the effects of memristive synapse's conductance gain, applied current, and the speed of electrical signal propagation along axons and dendrites on the system's behavior and the neuron's membrane potential are investigated. Analyzes are performed by investigating bifurcation and Lyapunov exponent diagrams versus various model parameters. The physiological role of some parameters and the effect of parameter changes on the model behaviors are discussed. The results demonstrate that when no current is applied to the system, the maximum value of membrane potential is larger, and also, a lower memristive synapse conductance gain leads to a larger maximum value of membrane potential. So, it can be concluded that the neuron in an amplitude death state may be triggered and start firing by decreasing the conductance gain or not applying current.