Topological stability criteria for networking dynamical systems with Hermitian Jacobian

A. L. Do, S. Boccaletti, J. Epperlein, S. Siegmund, T. Gross

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
229 Downloads (Pure)

Abstract

The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions that an interaction network has to obey in order to support a given type of macroscopic behaviour. The approach is based on a graphical notation, which allows rewriting Jacobi's signature criterion in an interpretable form and which can be applied to many systems of symmetrically coupled units. The derived conditions pertain to structures on all scales, ranging from individual nodes to the interaction network as a whole. For the purpose of illustration, we consider the example of synchronization, specifically the (heterogeneous) Kuramoto model and an adaptive variant. The results complete and extend the previous analysis of Do et al.

Original languageEnglish
Pages (from-to)888-903
Number of pages16
JournalEuropean Journal of Applied Mathematics
Volume27
Issue number6
DOIs
Publication statusPublished - 1 Dec 2016

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