Stability of networks of delay-coupled delay oscillators

Hofener, J. M.; Sethia, G. C.; Gross, T.

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Stability of networks of delay-coupled delay oscillators

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Sethia, G. C.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Gross, T.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Hofener, J. M., Sethia, G. C., & Gross, T. (2011). Stability of networks of delay-coupled delay oscillators. EPL, 95(4): 40002.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-8C6B-7

Abstract

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. Copyright (C) EPLA, 2011