ArticlePhysica D. Nonlinear phenomena2018
Global dynamics for switching systems and their extensions by linear differential equations.
Article in Physica D. Nonlinear phenomena, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits.Methods in molecular biology (Clifton, N.J.) · 2021Review
- Multi-parameter exploration of dynamics of regulatory networks.Bio Systems · 2020Review
- Multistability in the epithelial-mesenchymal transition network.BMC bioinformatics · 2020Article
- State-dependent effective interactions in oscillator networks through coupling functions with dead zones.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2019Article
- Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models.SIAM journal on applied dynamical systems · 2019Article
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Authors and funding
4 authors.
Funding
Abstract
Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.
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