# Delay-induced self-oscillation excitation in the FitzHugh-Nagumo model: regular and chaotic dynamics

## TL;DR

This paper explores how time-delayed feedback in the FitzHugh-Nagumo model induces both regular and chaotic self-oscillations, expanding understanding beyond noise control to deterministic chaos via numerical and analytical methods.

## Contribution

It demonstrates that delayed feedback can generate chaotic dynamics and chaos routes in the FitzHugh-Nagumo model, not just control coherence resonance.

## Key findings

- Delayed feedback induces regular and chaotic oscillations.
- Chaos can be achieved via a Feigenbaum route.
- Large delays produce pattern-like dynamics.

## Abstract

The stochastic FitzHugh-Nagumo model with time delayed-feedback is often studied in excitable regime to demonstrate the time-delayed control of coherence resonance. Here, we show that the impact of time-delayed feedback in the FitzHugh-Nagumo neuron is not limited by control of noise-induced oscillation regularity (coherence), but also results in excitation of the regular and chaotic self-oscillatory dynamics in the deterministic model. We demonstrate this numerically by means of simulations, linear stability analysis, the study of Lyapunov exponents and basins of attraction for both positive and negative delayed-feedback strengths. It has been established that one can implement a route to chaos in the explored model, where the intrinsic peculiarities of the Feigenbaum scenario are exhibited. For large time delay, we complement the study of temporal evolution by the interpretation of the dynamics as patterns in virtual space.