Functional Control of Oscillator Networks

TL;DR

This paper introduces a method to precisely control and stabilize functional patterns in oscillator networks by tuning local parameters, with applications in neuroscience and electrical grid management.

Contribution

It presents a novel, efficient approach to prescribe and analyze functional configurations in oscillator networks using algebraic and graph-theoretic conditions.

Findings

Successfully replicated cortical oscillation patterns.

Controlled power flow in electrical grid models.

Provided conditions for stability and feasibility.

Abstract

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators' parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators' phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.