Key motifs searching in complex dynamical systems

TL;DR

This paper introduces a novel energy-based method for identifying key motifs in complex dynamic systems, improving accuracy over traditional topology-based methods and aiding system control and understanding.

Contribution

It proposes a perturbation energy concept using the Jacobian matrix to define motif centrality, integrating network topology with dynamic equations.

Findings

Energy method yields more effective key motifs

Method maintains low algorithm complexity

Applicable to epidemic control and ecosystem protection

Abstract

Key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures. However, in dynamic systems, slight changes in the choice of dynamic equations and parameters can alter the significance of motifs. The known methods are insufficient to address this issue effectively. In this paper, we introduce a concept of perturbation energy based on the system's Jacobian matrix, and define motif centrality for dynamic systems by seamlessly integrating network topology with dynamic equations. Through simulations, we observe that the key motifs obtained by the proposed energy method present better effective and accurate than them by integrating network topology methods, without significantly increasing algorithm complexity. The finding of key motifs can be used to apply for system control, such as formulating containment policies for the spread of epidemics and protecting fragile ecosystems. Additionally, it makes substantial contribution to a deeper understanding of concepts in physics, such as signal propagation and system's stability.