  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.
