Noise-induced stabilization of the FitzHugh–Nagumo neuron dynamics: Multistability and transient chaos

Abstract

The nonlinear dynamics of a FitzHugh–Nagumo (FHN) neuron driven by an oscillating current and perturbed by a Gaussian noise signal with different intensities [Formula: see text] is investigated. In the noiseless case, stable periodic structures [Arnold tongues (ATS), cuspidal and shrimp-shaped] are identified in the parameter space. The periods of the ATSs obey specific generating and recurrence rules and are organized according to linear Diophantine equations responsible for bifurcation cascades. While for small values of [Formula: see text], noise starts to destroy elongations (“antennas”) of the cuspidals, for larger values of [Formula: see text], the periodic motion expands into chaotic regimes in the parameter space, stabilizing the chaotic motion, and a transient chaotic motion is observed at the periodic-chaotic borderline. Besides giving a detailed description of the neuronal dynamics, the intriguing novel effect observed for larger [Formula: see text] values is the generation of a regular dynamics for the driven FHN neuron. This result has a fundamental importance if the complex local dynamics is considered to study the global behavior of the neural networks when parameters are simultaneously varied, and there is the necessity to deal the intrinsic stochastic signal merged into the time series obtained from real experiments. As the FHN model has crucial properties presented by usual neuron models, our results should be helpful in large-scale simulations using complex neuron networks and for applications.