Noise-driven synchronization of a FitzHugh–Nagumo ring with phase-repulsive coupling: A perspective from the system’s nonequilibrium potential

Abstract

We study a one-dimensional array of N autonomous units with excitable FitzHugh–Nagumo dynamics coupled in phase-repulsive way to form a ring, and submitted to a common subthreshold harmonic signal and independent Gaussian white noises with a common intensity η . By varying η , two macroscopic regimes are observed. For some value of noise intensity, a transition from the rest state to an activated one–with almost half of the neurons excited forming an “...–activated–inhibited–activated–... ” structure along the ring–takes place. For larger values of η , the inverse transition is also observed, and both states alternate in a synchronized way with the signal. Moreover, measures of activation and coherent behavior become maximal for intermediate values of η . The origin of these collective effects is explained in terms of the system’s nonequilibrium potential. In particular, the levels of noise for activation and synchronization are theoretically estimated.