Stability of networks of delay-coupled delay oscillators
Biological Physics Section, Max-Planck-Institut für Physik komplexer Systeme Nöthnitzer Straß e 38, Dresden 01187, Germany, EU
2 Institute for Plasma Research - Bhat, Gandhinagar 382 428, India
Accepted: 29 June 2011
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.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 89.75.-k – Complex systems / 89.75.Hc – Networks and genealogical trees
© EPLA, 2011