Year: 2021
Type: article
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 are determined by a combinatorial analysis of the limiting switching system with piecewise constant nonlinearities. 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.
DOI: 10.1137/21m1398331
Authors: William Duncan, Tomas Gedeon, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: green
Awards: Dynamical Systems: New Developments in Theory and Application, G2515541506, G3749599873, Tripods+X:Res: Collaborative Research: Identification of Gene Regulatory Network Function from Data, G4713059963, Multilateral analysis of agglomeration over the entire area of China: construction of point GIS map of Chinese firms and spatial econometrics analysis, G5270150132, Toward the understanding of organizing center for the complex dynamics in dissipative systems, Cultivation of new methods for studying spatio-temporal rhythm dynamics through collaboration of theory and experiment, G668241585, G6823751671, HDR TRIPODS: Data Science Principles of the Human-Machine Convergence, Needle in a haystack: effective search for dynamics across the space of networks, Applications to the topological computation for coupled network dynamical systems of Large degrees of freedom, Achieving bipedal locomotion by using instability: Exploring the origin of human bipedalism, Tripods+X:Res: Collaborative Research: Identification of Gene Regulatory Network Function from Data
OpenAlex ID: W3206645419