title: Sufficient and necessary conditions for Lyapunov stability of genetic networks with SUM regulatory logic.
abstract: In this paper, a nonlinear model for genetic regulator networks (GRNs) with SUM regulatory logic is presented. Four sufficient and necessary conditions of global asymptotical stability and global exponential stability for the equilibrium point of the GRNs are proposed, respectively. Specifically, three weak sufficient conditions and corresponding corollaries are derived by using comparing theorem and Dini derivative method. Then, a famous GRN model is used as the example to illustrate the effectiveness of our theoretical results. Comparing to the results in the previous literature, some novel ideas, study methods and interesting results are explored.
authors.affiliation: Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China.
authors.forename: Guopeng
authors.initials: G
authors.lastname: Zhou
authors.affiliation: Department of Electric and Electronic Engineering, Wuhan Institute of Shipbuilding Technology, Wuhan, 430050 China.
authors.forename: Jinhua
authors.initials: J
authors.lastname: Huang
authors.affiliation: Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China.
authors.forename: Fengxia
authors.initials: F
authors.lastname: Tian
authors.affiliation: Institute of Engineering and Technology, Hubei University of Science and Technology, Xianning, 437100 China ; College of Automation, Huazhong University of Science and Technology, Wuhan, 430074 China.
authors.forename: Xiaoxin
authors.initials: X
authors.lastname: Liao
keywords: Asymptotical stability; Comparing theorem; Dini derivative; Exponential stability; Genetic regulator networks