Nonequilibrium potential for arbitrary-connected networks of FitzHugh–Nagumo elements

We study an array of N units with FitzHugh–Nagumo dynamics linearly coupled. The system is submitted to a subthreshold harmonic signal and independent Gaussian white noises with a common intensity η. In the limit of adiabatic driving, we analytically calculate the system’s nonequilibrium potential for arbitrary linear coupling. We illustrate its applicability by investigating noise-induced effects in an excitable regular network with extended antiphase coupling. In particular, the levels of noise for short-wavelength phase-instability, network’s synchronization and depinning of “defects” (groups of contiguous inhibited neurons on an antiphase background) are theoretically predicted and numerically confirmed. The origin of these collective effects and the dependence with parameters of the most probable length of defects are explained in terms of the system’s nonequilibrium potential.