Pattern formation in oscillatory complex networks consisting of excitable nodes

TL;DR

This paper investigates pattern formation in oscillatory complex networks with excitable nodes, revealing organized target waves from center nodes and providing methods to analyze, predict, and control these oscillations.

Contribution

It introduces a framework for understanding and predicting oscillation patterns in complex networks with excitable nodes, highlighting the role of skeleton structures and center nodes.

Findings

Oscillations originate from a few center nodes and small skeletons.

Target wave patterns propagate along shortest paths.

Analysis enables effective modulation of network oscillations.

Abstract

Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small skeletons for most oscillations. Complicated and seemingly random oscillatory patterns can be viewed as well-organized target waves propagating from center nodes along the shortest paths, and the shortest loops passing through both the center nodes and their driver nodes play the role of oscillation sources. Analyzing simple skeletons we are able to understand and predict various essential properties of the oscillations and effectively modulate the oscillations. These methods and results will give insights into pattern formation in complex networks, and provide suggestive ideas for studying and controlling oscillations in neural networks.