Global dynamics for steep nonlinearities in two dimensions

详细信息    查看全文

• 作者：Tomá ; &scaron ; Gedeon^a ; ^{gedeon@math.montana.edu} ; Shaun Harker^b ; ^{sharker81@gmail.com} ; Hiroshi Kokubu^c ; ^{kokubu@math.kyoto-u.ac.jp} ; Konstantin Mischaikow^b ; ^{mischaik@math.rutgers.edu} ; Hiroe Oka^d ; ^{oka@rins.ryukoku.ac.jp}
• 关键词：Switching systems ; Perturbation ; Morse graph ; Attractor filtration ; Robustness
• 刊名：Physica D: Nonlinear Phenomena
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：339
• 期：Complete
• 页码：18-38
• 全文大小：864 K
• 卷排序：339

文摘

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.