COLLECTIVE DYNAMICS IN AN ENSEMBLE OF GLOBALLY COUPLED FHN SYSTEMS

Abstract

We examine an ensemble of globally coupled FitzHugh–Nagumo systems with Gaussian, white noise. In the case of spatially uncorrelated noise, at high and at low noise levels the mean of the ensemble is steady. In between it exhibits a complex behavior. Depending on the noise intensity we find small scale oscillations, period doubling, chaos, and spiking. We derive equations of motion for the cumulants of the ensemble distribution. The results of the cumulant dynamics analysis are in good qualitative agreement with results from the Langevin dynamics. Once we additionally apply correlated noise but keep the sum of both noise intensities constant, the mean starts spiking where it did not spike with uncorrelated noise. For increasing correlation strength a minimum of the coefficient of variation appears.