The dynamics of networks of interacting systems depends intricately on theinteraction topology. When the dynamics is explored, generally the wholetopology has to be considered. However, we show that there are certainmesoscale subgraphs that have precise and distinct consequences for thesystem-level dynamics. In particular, if meso-scale symmetries are present theneigenvectors of the Jacobian localise on the symmetric subgraph and thecorresponding eigenvalues become insensitive to the topology outside thesubgraph. Hence, dynamical instabilities associated with these eigenvalues canbe analyzed without considering the topology outside the subgraph. While suchinstabilities are thus generated entirely in small network subgraphs, theygenerally do not remain confined to the subgraph once the instability sets inand thus have system-level consequences. Here we illustrate the analyticalinvestigation of such instabilities in an ecological meta-population modelconsisting of a network of delay-coupled delay oscillators.
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