Characterizing the dynamics of three FitzHugh-Nagumo neurons network

Abstract

The behavior of neuron systems can be modeled by the FitzHugh-Nagumo model, originally consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of three coupled neurons in a network modeled by the FitzHugh-Nagumo quations. We consider three neurons coupled unidirectionally and bidirectionally, for which Lyapunov diagrams were constructed calculating the Lyapunov exponents. The coupling parameter between neurons has an important role to the understanding of the physiological mechanisms of the nervous system. In this sense, the dynamics of the neural networks here investigated are presented in terms of the variation between the coupling strength of the neurons and other parameters of the system. The results show the occurrence of periodic structures embedded in chaotic regions, and also the existence of hyperchaos in their dynamics, besides, we show the importance of the type of coupling between the neurons, with respect to the existence of those behaviors for the same parameter set.