The paper demonstrates the possibility to control the collective behavior of a large network of excitable stochastic units, in which oscillations are induced merely by external random input. Each network element is represented by the FitzHugh-Nagumo system under the influence of noise, and the elements are coupled through the mean field. As known previously, the collective behavior of units in such a network can range from synchronous to non-synchronous spiking with a variety of states in between. We apply the Pyragas delayed feedback to the mean field of the network and demonstrate that this technique is capable of suppressing or weakening the collective synchrony, or of inducing the synchrony where it was absent. On the plane of control parameters we indicate the areas where suppression of synchrony is achieved. To explain the numerical observations on a qualitative level, we use the semi-analytic approach based on the cumulant expansion of the distribution density within Gaussian approximation. We perform bifurcation analysis of the obtained cumulant equations with delay and demonstrate that the regions of stability of its steady state have qualitatively the same structure as the regions of synchrony suppression of the original stochastic equations. We also demonstrate the delay-induced multistability in the stochastic network. These results are relevant to the control of unwanted behavior in neural networks.
- NONLINEAR OSCILLATORS