Vibrational Control of Complex Networks

TL;DR

This paper introduces a vibrational control method that manipulates network edges to stabilize complex systems, offering an open-loop alternative to traditional feedback strategies, with theoretical conditions and numerical validation.

Contribution

It presents a novel vibrational control approach focusing on edges rather than nodes, with graph-theoretic conditions and design methods for system stabilization.

Findings

Established sufficient conditions for vibration-induced network stabilization

Developed methods for designing effective vibrational inputs

Validated theoretical results through numerical simulations

Abstract

The stability of complex networks, from power grids to biological systems, is crucial for their proper functioning. It is thus important to control such systems to maintain or restore their stability. Traditional approaches rely on real-time state measurements for feedback control, but this can be challenging in many real-world systems, such as the brain, due to their complex and dynamic nature. This paper utilizes vibrational control -- an open-loop strategy -- to regulate network stability. Unlike conventional methods targeting network nodes, our approach focuses on manipulating network edges through vibrational inputs. We establish sufficient graph-theoretic conditions for vibration-induced functional modifications of network edges and stabilization of network systems as a whole. Additionally, we provide methods for designing effective vibrational control inputs and validate our theoretical findings through numerical simulations.