On the structural stability of random systems
Combinatorics
2020-03-26 v1 Probability
Abstract
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random structure. As is usually done, we describe the system's structure through a graph describing interactions between parts of the system, and we call a graph stable if it describe a structurally stable system, i.e., a system which can sustain stable dynamics. We then consider two Erdos-Renyi random graph models, and we obtain for each the probability that a graph sampled from these models is structurally stable.
Cite
@article{arxiv.2003.04139,
title = {On the structural stability of random systems},
author = {Mohamed Ali Belabbas and Artur Kirkoryan},
journal= {arXiv preprint arXiv:2003.04139},
year = {2020}
}