Global dynamics for steep nonlinearities in two dimensions

Tomáš Gedeon, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)18-38
Number of pages21
JournalPhysica D: Nonlinear Phenomena
StatePublished - Jan 15 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Attractor filtration
  • Morse graph
  • Perturbation
  • Robustness
  • Switching systems


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