Control of noise-induced behavior in neural network

Abstract

We study the effect of time-delayed feedback control on the noise-induced dynamics [1] of an ensemble of N globally coupled excitable neural oscillators, each being modeled by the FitzHugh–Nagumo system with independent Gaussian white noise source. Both coupling and feedback are introduced through the mean field. The effect of delayed feedback is studied both analytically and numerically. For the theoretical study we exploit a method of [2] introduced in [3], which allows one to write down a closed system of cumulant equations for the mean values, variances and covariances of the system variables, under the assumption that their third and higher order central moments are relatively small.[1] N.B. Janson, A.G. Balanov, E. Schöll, Phys. Rev. Lett. 93, 010601 (2004).[2] R. Rodriguez and H. C. Tuckwell, Phys. Rev. E 54, 5585 (1996).[3] S. Tanabe and K. Pakdaman, Phys. Rev. E 63, 031911 (2001)