Cooperative Dynamics in a Network of Stochastic Elements with Delayed Feedback.pdf

Cooperative Dynamics in a Network of Stochastic Elements with Delayed Feedback D. Huber and L. S. Tsimring Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402 (Dated: February 2, 2008) 5 0 Networks of globally coupled, noise activated, bistable elements with connection time delays are 0 considered. The dynamics of these systems is studied numerically using a Langevin description 2 and analytically using (1) a Gaussian approximation as well as (2) a dichotomous model. The system demonstrates ordering phase transitions and multi-stability. That is, for a strong enough r a feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function. Other observed dynamical phenomena include M coherence resonance and, in the case of non-uniform coupling strengths, amplitude death and chaos. 1 Furthermore, an increase of the stability of the trivial equilibrium with increasing non-uniformity 1 of the time delays is observed. ] PACS numbers: 05.45.Xt, 05.40.Ca, 02.30.Ks, 02.50.Ey h c e I. INTRODUCTION globally coupled network of phase oscillators has been m explored by Yeung and Strogatz [14], and Tsimring and t- Due to its relevance for a variety of scientific disciplines Pikovsky [19] studied the dynamics of a sing