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.
EPL (Europhysics Letters)
- Pub Date:
- August 2011
- Condensed Matter - Disordered Systems and Neural Networks;
- Nonlinear Sciences - Chaotic Dynamics;
- Quantitative Biology - Populations and Evolution