Synchronization in Networks of Linearly Coupled Dynamical Systems via Event-triggered Diffusions

TL;DR

This paper introduces event-triggered coupling strategies for synchronizing linearly coupled dynamical systems, ensuring synchronization under both continuous and discrete monitoring scenarios by using local neighborhood information.

Contribution

It proposes novel event-triggered diffusion coupling methods that guarantee synchronization in coupled systems with only local observations, extending existing synchronization techniques.

Findings

Synchronization is achieved under both continuous and discrete monitoring.

Event-triggered strategies reduce unnecessary communication.

Theoretical proofs confirm the effectiveness of the proposed methods.

Abstract

In this paper, we utilize event-triggered coupling configuration to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes of its neighborhood and the next observation time is triggered by the proposed criteria based on the local neighborhood information as well. Two scenarios are considered: continuous monitoring, that each node can observe its neighborhood's instantaneous states, and discrete monitoring, that each node can only obtain its neighborhood's states at the same time point when the coupling term is triggered. In both cases, we prove that if the system with persistent coupling can synchronize, then these event-trigger coupling strategies can synchronize the system, too.