On stability analysis of genetic regulatory networks represented by delay-differential equations

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”.