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Updated: Aug 15, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
Published on: December 7, 2021
Piecewise-linear models of genetic regulatory networks: equilibria and their stability
Richard Casey1, Hidde de Jong, Jean-Luc Gouzé
1COMORE INRIA, Unité de recherche Sophia Antipolis, 2004 route des Lucioles, BP 93, 06902, Sophia Antipolis, France.
Abstract:
A formalism based on piecewise-linear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be well-suited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion. We study the stability of equilibria (called singular equilibrium sets) that lie on the surfaces of discontinuity. We prove several theorems that characterize the stability of these singular equilibria directly from the state transition graph, which is a qualitative representation of the dynamics of the system. We also formulate a stronger conjecture on the stability of these singular equilibrium sets.
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