Synchrony suppression in ensembles of coupled oscillators via adaptive vanishing feedback

TL;DR

This paper presents a feedback control method with adaptive parameters to effectively suppress synchronization in ensembles of coupled oscillators, even under high system uncertainty and non-stationary conditions.

Contribution

It introduces an adaptive vanishing feedback approach that achieves desynchronization without detailed microscopic knowledge of the system.

Findings

Effective suppression of synchrony demonstrated in neuron models.

Method remains robust with non-stationary system parameters.

Stability analysis confirms the approach's reliability.

Abstract

Synchronization and emergence of a collective mode is a general phenomenon, frequently observed in ensembles of coupled self-sustained oscillators of various natures. In several circumstances, in particular in cases of neurological pathologies, this state of the active medium is undesirable. Destruction of this state by a specially designed stimulation is a challenge of high clinical relevance. Typically, the precise effect of an external action on the ensemble is unknown, since the microscopic description of the oscillators and their interactions are not available. We show, that desynchronization in case of a large degree of uncertainty about important features of the system is nevertheless possible; it can by achieved by virtue of a feedback loop with an additional adaptation of parameters. The adaptation also ensures desynchronization of ensembles with non-stationary, time-varying parameters. We perform the stability analysis of the feedback-controlled system and demonstrate efficient destruction of synchrony for several models, including those of spiking and bursting neurons.