Amplitude death in networks of delay-coupled delay oscillators
arXiv:1210.2002 · doi:10.1098/rsta.2012.0462
Abstract
Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical results for degree homogeneous networks that show that amplitude death is governed by certain eigenvalues of the network's adjacency matrix. In particular these results demonstrate that in delay-coupled delay oscillators amplitude death can occur for arbitrarily large coupling strength k. In this limit we find a region of amplitude death, which occurs already at small coupling delays that scale with 1/k. We show numerically that these results remain valid in random networks with heterogeneous degree distribution.
9 pages, 3 figures
References in corpus (7)
- Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
- Delays, connection topology, and synchronization of coupled chaotic maps
- Generalized models as a universal approach to the analysis of nonlinear dynamical systems
- Total and partial amplitude death in networks of diffusively coupled oscillators
- Synchronizability of chaotic logistic maps in delayed complex networks
- Control of unstable steady states in neutral time-delayed systems
- Stability of networks of delay-coupled delay oscillators