Engineering mesoscale structures with distinct dynamical implications in networks of delaycoupled delay oscillators
Abstract
The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, we show that there are certain mesoscale subgraphs that have precise and distinct consequences for the systemlevel dynamics. In particular, if mesoscale symmetries are present then eigenvectors of the Jacobian localise on the symmetric subgraph and the corresponding eigenvalues become insensitive to the topology outside the subgraph. Hence, dynamical instabilities associated with these eigenvalues can be analyzed without considering the topology outside the subgraph. While such instabilities are thus generated entirely in small network subgraphs, they generally do not remain confined to the subgraph once the instability sets in and thus have systemlevel consequences. Here we illustrate the analytical investigation of such instabilities in an ecological metapopulation model consisting of a network of delaycoupled delay oscillators.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1207.1319
 Bibcode:
 2012arXiv1207.1319D
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Mathematics  Dynamical Systems
 EPrint:
 15 pages, 3 figures, 1 table