2002/07/31 by Marc Timme, Fred Wolf, Theo Geisel · 1 citation
Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #cond-mat.dis-nn #q-bio.NC
paper · pdf · doi:10.1103/physrevlett.89.258701
published as Phys. Rev. Lett. 89, 258701 (2002) · 4 pages, 2 figures
arxiv created 2003/03/17 · arxiv updated 2009/11/30
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multi-operator problem analytically and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state that exhibits irregular dynamics such that external signals may switch the network between qualitatively distinct states.