Phase noise induced single or double coherence resonances of neural firing

Neuronal firing activity can be changed from the resting state to firing state either through Hopf bifurcation where the firing exhibits a fixed period or through saddle-node bifurcation where the firing frequency is nearly zero. Phase noise with periodicity can induce coherence resonances near Hopf and saddle-node bifurcation points. When the period of phase noise is shorter than the internal period of firing near the Hopf bifurcation point, the phase noise can induce single coherence resonance appearing near the frequency of the phase noise. When the period of phase noise is longer than the internal period of firing near the Hopf bifurcation point, the phase noise can induce double coherence resonances. The resonance at low noise intensity appears near the frequency of the phase noise, and the one at large noise intensity occurs near the frequency of the firing near the Hopf bifurcation. The mechanism of the double resonances is explained. Unlike the Hopf bifurcation point, only a single coherence resonance can be induced near the saddle-node bifurcation point by the phase noise with long or short periods. The results not only reveal the dynamics of phase noise induced coherence resonance of the equilibrium point and identify the distinction between two types of neuronal excitabilities corresponding to two kinds of bifurcations, but also provide an explanation about the different results of phase noise induced single or double resonances simulated in recent studies.