Dynamics of Delay Equations, Theory and Applications - Abstract

Gjurchinovski, Aleksandar

Amplitude death in complex networks with time-varying delayed coupling

joint work with Anna Zakharova and Eckehard Sch"oll, Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany We propose a method to control amplitude death in networks of delay-coupled limit cycle oscillators with a time-varying delay in the coupling. We consider the impact of the variability of the time delay in the node interconnections, as well as in the self-feedback, either at each node or at a single node only. To investigate analytically the regions of amplitude death in the parameter space, we generalize the formalism of the master stability function, which is a method originally used to analyze the synchronous dynamics of complex networks. At high-frequency delay modulation, analytical results for the occurrence of amplitude death can be obtained by approximating the variable-delay coupling terms by distributed delay with delay-distribution kernels matching the probability density function. The superiority of the proposed method with respect to the constant delay case is demonstrated both numerically and analytically for a regular ring network consisting of Stuart-Landau limit cycle oscillators in the regime near a Hopf bifurcation.