Amplitude death and restoration in networks of oscillators with random-walk diffusion
Abstract
We study the death and restoration of collective oscillations in networks of oscillators coupled through random-walk diffusion. Differently than the usual diffusion coupling used to model chemical reactions, here the equilibria of the uncoupled unit is not a solution of the coupled ensemble. Instead, the connectivity modifies both, the original unstable fixed point and the stable limit-cycle, making them node-dependent. Using numerical simulations in random networks we show that, in some cases, this diffusion induced heterogeneity stabilizes the initially unstable fixed point via a Hopf bifurcation. Further increasing the coupling strength the oscillations can be restored as well. Upon numerical analysis of the stability properties we conclude that this is a novel case of amplitude death. Finally we use a heterogeneous mean-field reduction of the system in order to proof the robustness of this phenomena upon increasing the system size.
Keywords
Cite
@article{arxiv.2009.04740,
title = {Amplitude death and restoration in networks of oscillators with random-walk diffusion},
author = {Pau Clusella and M. Carmen Miguel and Romualdo Pastor-Satorras},
journal= {arXiv preprint arXiv:2009.04740},
year = {2021}
}