The chaotic dynamics and multistability of two coupled Fitzhugh–Nagumo model neurons

Abstract

In this short article, we present a detailed analysis of the dynamics of a system of two coupled Fitzhugh–Nagumo neuron equations with tonic descending command signals, suitable for modelling circuits underlying the generation of motor behaviours. We conduct a search of possible attractors and calculate dynamical quantities, such as the largest Lyapunov exponents (LLEs), at a fine resolution over the areas of parameter space where complex and chaotic dynamics are most likely, to build a more detailed picture of the dynamical regimes of the system, focusing on the most complex solutions. By building a precise LLE map, we identify a narrow region of parameter space of particular interest, rich with chaotic and multistable dynamics, and show that it is on the border of criticality. This allows us to draw conclusions about possible neural mechanisms underlying the generation of chaotic dynamics. We illustrate the detailed ecology of multiple attractors in the system by listing, characterising and grouping all the stable attractors in the parameter range of interest. This allows us to pinpoint the regions with complex multistability. The greater understanding thus provided is intended to help future studies on the roles of chaotic dynamics in biological motor control, and their application in robotics, particularly by giving a deeper insight into how input signals and control parameters shape the system’s dynamics which can be exploited in chaos-driven adaptation.