2013/02/28 by Otti D’Huys, Otti D'Huys, D'Huys, Otti +8
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence #nlin.CD
paper · pdf · doi:10.48550/arxiv.1302.7277
arxiv created 2013/02/28 · openalex publication_date 2013/02/28 · arxiv updated 2013/03/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in such systems possesses a hierarchical structure, with different parts scaling with the different delays. This leads to different types of chaos, depending on the scaling of the maximal LE. Our results are relevant, in particular, for the synchronization properties of hierarchical networks (networks of networks) where the nodes of subnetworks are coupled with shorter delays and couplings between different subnetworks are realized with longer delay times. Units within a subnetwork can synchronize if the maximal exponent scales with the shorter delay, long range synchronization between different subnetworks is only possible if the maximal exponent scales with the long delay. The results are illustrated analytically for Bernoulli maps and numerically for tent maps.