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dc.contributor.authorDuncan, William
dc.contributor.authorGedeon, Tomas
dc.identifier.citationDuncan, 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.descriptionElectronic version of an article published as International Journal of Bifurcation and Chaos, 31, 11, 2021, 10.1142/S0218127421300329 © World Scientific Publishing Company
dc.description.abstractIn 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.publisherWorld Scientific Pub Co Pte Lten_US
dc.rightscopyright World Scientific Pub Co Pte Lt 2021en_US
dc.rights.uriWorld Scientific Pub Co Pte Lten_US
dc.subjectregulatory networken_US
dc.subjectswitching systemen_US
dc.subjectcyclic feedback systemen_US
dc.titleStability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactionsen_US
mus.citation.journaltitleInternational Journal of Bifurcation and Chaosen_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US

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