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dc.contributor.authorCrawford-Kahrl, Peter
dc.contributor.authorCummins, Bree
dc.contributor.authorGedeon, Tomáš
dc.date.accessioned2019-06-05T17:44:05Z
dc.date.available2019-06-05T17:44:05Z
dc.date.issued2019-04
dc.identifier.citationCrawford-Kahrl, Peter, Bree Cummins, and Tomas Gedeon. "Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models." Siam Journal on Applied Dynamical Systems 18, no. 1 (April 2019): 418-457. DOI:10.1137/18M1163610.en_US
dc.identifier.issn1536-0040
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/15488
dc.description.abstractModeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous time switching systems provide a computationally accessible way to translate the structure of the network to predictions about the dynamics. Recent work has shown that the parameterized dynamics of switching systems can be captured by a combinatorial object, called a Dynamic Signatures Generated by Regulatory Networks (DSGRN) database, that consists of a parameter graph characterizing a finite parameter space decomposition, whose nodes are assigned a Morse graph that captures global dynamics for all corresponding parameters. We show that for a given network there is a way to associate the same type of object by considering a continuous time ODE system with a continuous right-hand side, which we call an L-system. The main goal of this paper is to compare the two DSGRN databases for the same network. Since the L-systems can be thought of as perturbations (not necessarily small) of the switching systems, our results address the correspondence between global parameterized dynamics of switching systems and their perturbations. We show that, at corresponding parameters, there is an order preserving map from the Morse graph of the switching system to that of the L-system that is surjective on the set of attractors and bijective on the set of fixed-point attractors. We provide important examples showing why this correspondence cannot be strengthened.en_US
dc.description.sponsorshipMontana State University; DARPA (D12AP200025, FA8750-17-C-0054); NIH (1R01GM126555-01, 1R01AG040020-01, P20GM103474); NSF (DMS-1226213, DMS-1361240); USDA (2015-51106-23970)en_US
dc.rightsThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en_US
dc.titleComparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Modelsen_US
dc.typeArticleen_US
mus.citation.extentfirstpage418en_US
mus.citation.extentlastpage457en_US
mus.citation.issue1en_US
mus.citation.journaltitleSiam Journal on Applied Dynamical Systemsen_US
mus.citation.volume18en_US
mus.identifier.categoryPhysics & Mathematicsen_US
mus.identifier.doi10.1137/18M1163610en_US
mus.relation.collegeCollege of Letters & Scienceen_US
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US
mus.data.thumbpage24en_US


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