Global Dynamics for Steep Nonlinearities in Two Dimensions


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


Physica D. Nonlinear phenomena


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.



How is this information collected?

This collection of Montana State authored publications is collected by the Library to highlight the achievements of Montana State researchers and more fully understand the research output of the University. They use a number of resources to pull together as complete a list as possible and understand that there may be publications that are missed. If you note the omission of a current publication or want to know more about the collection and display of this information email Leila Sterman.