Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions
Dynamical Systems
2015-08-12 v1
Abstract
We introduce a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. Motivated by models of regulatory networks, we construct a state transition graph from a piecewise affine ordinary differential equation. We use efficient graph algorithms to compute an associated Morse graph that codifies the recurrent and gradient-like dynamics. We prove that for 2-dimensional systems, the Morse graph defines a Morse decomposition for the dynamics of any smooth differential equation that is sufficiently close to the original piecewise affine ordinary differential equation.
Cite
@article{arxiv.1508.02438,
title = {Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions},
author = {Tomas Gedeon and Shaun Harker and Hiroshi Kokubu and Konstantin Mischaikow and Hiroe Oka},
journal= {arXiv preprint arXiv:1508.02438},
year = {2015}
}