Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1912337259