Bifurcations and resonances in a birhythmic Hindmarsh-Rose neuron model with different spikes

The birhythmic Hindmarsh-Rose model, characterized by limit cycles with different spikes, is investigated for its bifurcations and resonances, and stochastic sensitivity analysis is performed. The study indicates that the stationary probability density changes by selecting the noise level and the system parameter as bifurcation parameters, signifying the emergence of stochastic phenomenological bifurcation. By increasing the noise, changes in the sign of the largest Lyapunov exponent reveal that the system experiences stochastic dynamical bifurcation. The stochastic sensitivity analysis is utilized as well to explore the dispersion of stochastic solutions around the limit cycle. This paper identifies both anticoherence resonance and coherence resonance induced by noise, as revealed by the coefficient of variation. Furthermore, considering the response to the harmonic signal, noise-induced suppression as well as stochastic resonance phenomena are revealed by analyzing the signal-to-noise ratio. Studying the stochastic dynamical behavior of Hindmarsh-Rose neuron model can provide better insights into how neurons respond to noise, aiding in the simulation and analysis of neuronal activity in neurological disease states.