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

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.