Dynamics of delay-coupled excitable neural systems

TL;DR

This paper investigates how delay coupling affects the dynamics of excitable neural systems, revealing bistability and delay-induced oscillations through bifurcation analysis.

Contribution

It introduces a detailed analysis of delay-induced phenomena in FitzHugh-Nagumo neural models, highlighting the role of saddle-node bifurcations in bistability and oscillations.

Findings

Bistability between fixed point and limit cycle occurs at large delays and coupling.

Delay-induced oscillations are caused by saddle-node bifurcations of limit cycles.

Delay parameters critically influence neural system dynamics.

Abstract

We study the nonlinear dynamics of two delay-coupled neural systems each modelled by excitable dynamics of FitzHugh-Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for sufficiently large delay times and coupling strength. As the mechanism for these delay-induced oscillations we identify a saddle-node bifurcation of limit cycles.