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arXiv · 2103.17184

Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities

William Duncan·Tomas Gedeon·Hiroshi Kokubu·Konstantin Mischaikow·Hiroe Oka
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Abstract

In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by a sigmoidal nonlinear function. We show that the existence and stability of equilibria of a sigmoidal system is determined by a combinatorial analysis of the limiting switching system with piece-wise constant non-linearities. In addition, we describe a local decomposition of a switching system into a product of simpler cyclic feedback systems, where the cycles in each decomposition correspond to a particular subset of network loops.

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William Duncan, Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka. 2021-03-31. Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities. https://arxiv.org/abs/2103.17184

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