Modularity and the spread of perturbations in complex dynamical systems.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Artemy KolchinskyLuis M Rocha

Abstract

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Ou...Continue Reading

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Citations

Jul 25, 2019·Physical Review. E·Michael T SchaubMauricio Barahona
Mar 20, 2021·Proceedings of the National Academy of Sciences of the United States of America·Alexander J GatesLuis M Rocha

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