Vibrational Control of Cluster Synchronization: Connections with Deep Brain Stimulation

TL;DR

This paper explores how vibrational control techniques can influence cluster synchronization in brain networks, providing theoretical conditions and design methods, with implications for understanding deep brain stimulation mechanisms.

Contribution

It introduces vibrational control as a model for deep brain stimulation effects on neuronal synchrony within Kuramoto-oscillator networks, offering new theoretical insights.

Findings

Vibrational control can stabilize cluster synchronization.

Derived sufficient conditions for vibrational stabilization.

Numerical example supports theoretical results.

Abstract

Cluster synchronization underlies various functions in the brain. Abnormal patterns of cluster synchronization are often associated with neurological disorders. Deep brain stimulation (DBS) is a neurosurgical technique used to treat several brain diseases, which has been observed to regulate neuronal synchrony patterns. Despite its widespread use, the mechanisms of DBS remain largely unknown. In this paper, we hypothesize that DBS plays a role similar to vibrational control since they both highly rely on high-frequency excitation to function. Under the framework of Kuramoto-oscillator networks, we study how vibrations introduced to network connections can stabilize cluster synchronization. We derive some sufficient conditions and also provide an effective approach to design vibrational control. Also, a numerical example is presented to demonstrate our theoretical findings.