Controlling synchrony in oscillatory networks via an act-and-wait algorithm

Abstract

The act-and-wait control algorithm is proposed to suppress synchrony in globally coupled oscillatory networks in the situation when the simultaneous registration and stimulation of the system is not possible. The algorithm involves the periodic repetition of the registration (wait) and stimulation (act) stages, such that in the first stage the mean field of the free system is recorded in a memory and in the second stage the system is stimulated with the recorded signal. A modified version of the algorithm that takes into account the charge-balanced requirement is considered as well. The efficiency of our algorithm is demonstrated analytically and numerically for globally coupled Landau-Stuart oscillators and synaptically all-to-all coupled FitzHugh-Nagumo as well as Hodgkin-Huxley neurons.

Eliminating synchronization in bistable networks

“…Recently we have applied this algorithm to monostable oscillatory networks, which possess stable coherent and unstable incoherent states, and shown that it can effectively stabilize the incoherent state [35]. Now we verify the capability of this algorithm to switch a bistable network from the stable coherent state to the stable incoherent state.…”

“…Now we verify the capability of this algorithm to switch a bistable network from the stable coherent state to the stable incoherent state. As applied to neural networks, the act-and-wait algorithm is formulated as follows (see [35] for details). It is assumed that only mean field of the network is available for observation and only homogeneous perturbations are allowed.…”

“…Nonfeedback algorithms are mainly based on a phase resetting stimulation [27][28][29]. The closed loop control methods are more diversified; they include linear [30][31][32][33][34][35] and nonlinear [36][37][38] time-delayed feedback control algorithms as well as other approaches [39][40][41][42][43][44]. All these algorithms have been developed to networks, which possess a stable coherent state and an unstable incoherent state.…”

“…In this paper, we describe two strategies for controlling synchronization in bistable networks. The first strategy is based on an act-and-wait control algorithm [35,[46][47][48][49], which represents a timedelayed feedback control with a periodically switched on and off control gain. The second strategy utilizes a nonfeedback multisite coordinated reset (MCR) stimulation algorithm [28,29].…”

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

“…A number of more sophisticated methods to avoid synchronization of interacting oscillators in general and more specifically with the possible application to neuronal arrays have been described in literature, for example [33,37,[44][45][46][47][48][49][50][51][52][53][54].…”