4 research outputs found
Complex oscillations in the delayed Fitzhugh-Nagumo equation
Motivated by the dynamics of neuronal responses, we analyze the dynamics of
the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system
provides a canonical example of a canard explosion for sufficiently small
delays. Beyond this regime, delays significantly enrich the dynamics, leading
to mixed-mode oscillations, bursting and chaos. These behaviors emerge from a
delay-induced subcritical Bogdanov-Takens instability arising at the fold
points of the S-shaped critical manifold. Underlying the transition from
canard-induced to delay-induced dynamics is an abrupt switch in the nature of
the Hopf bifurcation
Delay-induced self-oscillation excitation in the FitzHugh-Nagumo model: regular and chaotic dynamics
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.Comment: 12 pages, 11 figures in the main text and 3 figures in appendi