Delay-induced self-oscillation excitation in the Fitzhugh–Nagumo model: Regular and chaotic dynamics

Vladimir V. Semenov, Andrei V. Bukh and Nadezhda Semenova

Chaos, Solitons & Fractals, 2023, vol. 172, issue C

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.

Keywords: FitzHugh–Nagumo model; Excitable regime; Time delay; Delay-induced self-oscillations; Delay-induced chaos; Dissipative solitons (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004253

DOI: 10.1016/j.chaos.2023.113524

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