dc.contributor.author Duncan, William dc.contributor.author Gedeon, Tomas dc.date.accessioned 2022-09-23T15:07:42Z dc.date.available 2022-09-23T15:07:42Z dc.date.issued 2021-09 dc.identifier.citation Duncan, W., & Gedeon, T. (2021). Stability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactions. International Journal of Bifurcation and Chaos, 31(11), 2130032. en_US dc.identifier.issn 0218-1274 dc.identifier.uri https://scholarworks.montana.edu/xmlui/handle/1/17210 dc.description Electronic version of an article published as International Journal of Bifurcation and Chaos, 31, 11, 2021, 10.1142/S0218127421300329 © World Scientific Publishing Company https://doi.org/10.1142/S0218127421300329 en_US dc.description.abstract In this paper, we study equilibria of differential equation models for networks. When interactions between nodes are taken to be piecewise constant, an efficient combinatorial analysis can be used to characterize the equilibria. When the piecewise constant functions are replaced with piecewise linear functions, the equilibria are preserved as long as the piecewise linear functions are sufficiently steep. Therefore the combinatorial analysis can be leveraged to understand a broader class of interactions. To better understand how broad this class is, we explicitly characterize how steep the piecewise linear functions must be for the correspondence between equilibria to hold. To do so, we analyze the steady state and Hopf bifurcations which cause a change in the number or stability of equilibria as slopes are decreased. Additionally, we show how to choose a subset of parameters so that the correspondence between equilibria holds for the smallest possible slopes when the remaining parameters are fixed. en_US dc.language.iso en_US en_US dc.publisher World Scientific Pub Co Pte Lt en_US dc.rights copyright World Scientific Pub Co Pte Lt 2021 en_US dc.rights.uri World Scientific Pub Co Pte Lt en_US dc.subject regulatory network en_US dc.subject bifurcation en_US dc.subject switching system en_US dc.subject cyclic feedback system en_US dc.title Stability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactions en_US dc.type Book en_US mus.citation.extentfirstpage 1 en_US mus.citation.extentlastpage 32 en_US mus.citation.issue 11 en_US mus.citation.journaltitle International Journal of Bifurcation and Chaos en_US mus.citation.volume 31 en_US mus.identifier.doi 10.1142/S0218127421300329 en_US mus.relation.college College of Letters & Science en_US mus.relation.department Mathematical Sciences. en_US mus.relation.university Montana State University - Bozeman en_US mus.data.thumbpage 6 en_US
﻿

### This item appears in the following Collection(s)

MSU uses DSpace software, copyright © 2002-2017  Duraspace. For library collections that are not accessible, we are committed to providing reasonable accommodations and timely access to users with disabilities. For assistance, please submit an accessibility request for library material.