Stability Boundaries in Second-order Time-delayed Networks with Symmetry
Chaotic Dynamics
2017-08-15 v1 Dynamical Systems
Abstract
In this contribution we aim to study the stability boundaries of solutions at equilibria for a second-order oscillator networks with SN-symmetry, we look for non-degenerate Hopf bifurcations as the time-delay between nodes increases. The remarkably simple stability criterion for synchronous solutions which, in the case of first-order self-oscillators, states that stability depends only on the sign of the coupling function derivative, is extended to a generic coupling function for second-order oscillators. As an application example, the stability boundaries for a N-node Phase-Locked Loop network is analysed.
Cite
@article{arxiv.1708.03931,
title = {Stability Boundaries in Second-order Time-delayed Networks with Symmetry},
author = {Diego Paolo Ferruzzo Correa and José Roberto Castilho Piqueira},
journal= {arXiv preprint arXiv:1708.03931},
year = {2017}
}
Comments
Research paper, 11 pages