Stability of networks of delay-coupled delay oscillators

Details Stability of networks of delay-coupled delay oscillators Stability of networks of delay-coupled delay oscillators

2010-10-18

arxiv.org/abs/1010.3557v2

EPL95(2011)40002

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1209/0295-5075/95/40002

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed. Exploiting a link between structure and dynamics, we identify conditions under which perturbations of the topology have a strong impact on the stability. If these critical regions are avoided the local stability of large random networks can be well approximated analytically.

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