Global dynamics for steep nonlinearities in two dimensions

PHYSICA D-NONLINEAR PHENOMENA

卷:339

Article

Gedeon, Tomas¹  Harker, Shaun²  Kokubu, Hiroshi³  Mischaikow, Konstantin²  Oka, Hiroe⁴ 

[1] Montana State Univ, Dept Math Sci, Bozeman, MT 59715 USA

[2] Rutgers State Univ, Dept Math, Hill Ctr, Busch Campus, Piscataway, NJ 08854 USA

[3] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

[4] Ryukoku Univ, Dept Appl Math & Informat, Otsu, Shiga 5202194, Japan

关键词: Switching systems;    Perturbation;    Morse graph;    Attractor filtration;    Robustness;   

DOI  :  10.1016/j.physd.2016.08.006

来源: Elsevier

【 摘 要 】

This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we associate a Morse graph, a computable object that describes a Morse decomposition of the dynamics. In this paper we show that all smooth perturbations of the switching system share the same Morse graph and we compute explicit bounds on the size of the allowable perturbation. This shows that computationally tractable switching systems can be used to characterize dynamics of smooth systems with steep nonlinearities. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free