Stability of piecewise-linear models of genetic regulatory networks

doi:10.1088/1674-1056/20/10/108701

Abstract This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero.

Keywords: genetic regulatory networks piecewise-linear model Lyapunov function

Received: 29 November 2010
Revised: 13 April 2011
Accepted manuscript online:

PACS:	87.18.Vf	(Systems biology)
	87.85.Xd	(Dynamical, regulatory, and integrative biology)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60672029).

Cite this article:

Lin Peng(林鹏), Qin Kai-Yu(秦开宇), and Wu Hai-Yan(吴海燕) Stability of piecewise-linear models of genetic regulatory networks 2011 Chin. Phys. B 20 108701

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