Vibrational Stabilization of Cluster Synchronization in Oscillator Networks

TL;DR

This paper introduces a vibrational control method to stabilize cluster synchronization in oscillator networks without requiring state measurements, addressing challenges in real-world systems like neural networks.

Contribution

It develops a novel open-loop vibrational control approach with sufficient conditions for stabilization, applicable when system states are difficult to measure.

Findings

Vibrational inputs can stabilize cluster synchronization.

The paper provides a practical design method for vibrational control.

Numerical experiments validate the theoretical results.

Abstract

Cluster synchronization is of paramount importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as neurological disorders in the brain. Therefore, it is crucial to restore normal system functions by stabilizing the appropriate cluster synchronization patterns. Most existing studies focus on designing controllers based on state measurements to achieve system stabilization. However, in many real-world scenarios, measuring system states, such as neuronal activity in the brain, poses significant challenges, rendering the stabilization of such systems difficult. To overcome this challenge, in this paper, we employ an open-loop control strategy, vibrational control, which does not requires any state measurements. We establish some sufficient conditions under which vibrational inputs stabilize cluster synchronization. Further, we provide a tractable approach to design vibrational control. Finally, numerical experiments are conducted to demonstrate our theoretical findings.