On stability analysis of genetic regulatory networks represented by delay-differential equations. Issue 1 (2015)

• Record Type: Journal Article
• Authors: Haustenne, Laurie; Bastin, Georges; Coron, Jean-Michel; Fontaine, Laetitia; Hols, Pascal
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 1(2015)
• Page Start: 453
• Page End: 457
• Publication Date: 2015
• Subjects: Genetic regulatory network -- Hyperbolic system -- Lyapunov function -- Stability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.05.108
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The purpose of this note is to give a short presentation of a general method for the stability analysis of the steady-states of genetic regulatory networks represented by delay- differential equations. Two complementary ways are investigated: a frequency domain approach which applies to linearized models and gives necessary and sufficient conditions for the local steady-state stability, a Lyapunov approach derived from the viewpoint of hyperbolic PDE systems which gives sufficient conditions for global stability. These methods are illustrated with the example of the "toggle switch".