Local control of an array of the diffusively coupled FitzHugh–Nagumo oscillators via repulsive mean field

Abstract

A feedback method for stabilizing the steady states in an array of the coupled nonlinear oscillators is described. The method employs two complementary techniques: the pinning control accomplished via a single accidentally accessed (or randomly chosen) oscillator and the repulsive mean field. Analytical, numerical, and experimental results are presented for a chain of the diffusively coupled FitzHugh–Nagumo (FHN) type oscillators with an exponential activation function. The experiment has been performed using analog electrical circuit, imitating dynamical behavior of the spiking FHN oscillators.