Quiver representations and dimension reduction in dynamical systems
Dynamical Systems
2020-09-22 v2
Abstract
Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry and feedforward structure, as well as subnetwork and quotient relations in network dynamical systems. A quiver equivariant dynamical system consists of a collection of dynamical systems with maps between them that send solutions to solutions. We prove that such quiver structures are preserved under Lyapunov-Schmidt reduction, center manifold reduction, and normal form reduction.
Cite
@article{arxiv.2006.08073,
title = {Quiver representations and dimension reduction in dynamical systems},
author = {Eddie Nijholt and Soeren Schwenker and Bob Rink},
journal= {arXiv preprint arXiv:2006.08073},
year = {2020}
}
Comments
Revised version, accepted in the SIAM Journal on Applied Dynamical Systems; 43 pages, 10 figures