Global dynamics for steep nonlinearities in two dimensions

被引:22
作者
Gedeon, Tomas [1 ]
Harker, Shaun [2 ]
Kokubu, Hiroshi [3 ]
Mischaikow, Konstantin [2 ]
Oka, Hiroe [4 ]
机构
[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
基金
美国国家科学基金会;
关键词
Switching systems; Perturbation; Morse graph; Attractor filtration; Robustness;
D O I
10.1016/j.physd.2016.08.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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.
引用
收藏
页码:18 / 38
页数:21
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