Coherence resonance in excitable and oscillatory systems: the essential role of slow and fast dynamics

Stochastic noise of an appropriate amplitude can maximize the coherence of the dynamics of certain types of excitable systems via a phenomenon known as coherence resonance (CR). In this paper we demonstrate, using a simple excitable system, the mechanism underlying the generation of CR. Using analytical expressions for the spectral density of the system's dynamics, we show that CR relies on the coexistence of fast and slow motions. We also show that the same mechanism of CR holds in the oscillatory regime, and we examine how CR depends on both the excitability of the system and the nonuniformity of the motion.