Noise-induced excitation wave and its size distribution in coupled FitzHugh-Nagumo equations on a square lattice.

There are various research topics such as stochastic resonance, coherent resonance, and neuroavalanche in excitable systems under external noises. We perform numerical simulation of coupled noisy FitzHugh-Nagumo equations on the square lattice. Excitation waves are generated most efficiently at an intermediate noise strength. The cluster size distributions obey a power-law-like distribution at a certain parameter range. However, we consider that this is not a self-organized critical phenomenon, partly because the exponent of the power law is not constant. We have studied the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equations with a one-dimensional pacemaker region and found that there is a phase-transition-like phenomenon from the short-range propagation to the whole-system propagation by changing the noise strength T. The power-law distribution is observed most clearly near the phase transition of the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equations without the one-dimensional pacemaker.