Stability of piecewise-linear models of genetic regulatory networks

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

中国物理B ›› 2011, Vol. 20 ›› Issue (10): 108701-108701.doi: 10.1088/1674-1056/20/10/108701

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

Stability of piecewise-linear models of genetic regulatory networks

林鹏, 秦开宇, 吴海燕

Institute of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu 610054, China

收稿日期:2010-11-29 修回日期:2011-04-13 出版日期:2011-10-15 发布日期:2011-10-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60672029).

Stability of piecewise-linear models of genetic regulatory networks

Lin Peng(林鹏)^†, Qin Kai-Yu(秦开宇), and Wu Hai-Yan(吴海燕)

Institute of Astronautics and Aeronautics, University of Electronic Science and Technology of China, Chengdu 610054, China

Received:2010-11-29 Revised:2011-04-13 Online:2011-10-15 Published:2011-10-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60672029).

摘要/Abstract

摘要： 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.

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.

Key words: genetic regulatory networks, piecewise-linear model, Lyapunov function

中图分类号: (Systems biology)

87.18.Vf

87.85.Xd (Dynamical, regulatory, and integrative biology)

林鹏, 秦开宇, 吴海燕. Stability of piecewise-linear models of genetic regulatory networks[J]. 中国物理B, 2011, 20(10): 108701-108701.

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[J]. Chin. Phys. B, 2011, 20(10): 108701-108701.

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Stability of piecewise-linear models of genetic regulatory networks

Stability of piecewise-linear models of genetic regulatory networks

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