M-matrix-based globally asymptotic stability criteria for genetic regulatory networks with time-varying discrete and unbounded distributed delays

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• 作者：Xian Zhang^a ; ^{xianzhang@ieee.org" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Yuanyuan Han^a ; ^{1056954098@qq.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Ligang Wu^b ; ^{ligangwu@hit.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Jiahua Zou^a ; ^{726489129@qq.com" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Genetic regulatory networks (GRNs) ; Time-varying discrete delays ; Unbounded distributed delays ; Globally asymptotic stability ; M-matrix-based approach
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：22 January 2016
• 年：2016
• 卷：174
• 期：part_PB
• 页码：1060-1069
• 全文大小：906 K

文摘

The problem of globally asymptotic stability for nonnegative equilibrium points of genetic regulatory networks (GRNs) with time-varying discrete delays and unbounded distributed delays is considered. So far, there are very few results concerning the problem; and in which the nonnegativity of equilibrium points is neglected. In this paper, the existence of nonnegative equilibrium points is firstly presented. Then, by using the nonsingular M-matrix theory and the functional differential equation theory, M-matrix-based sufficient conditions are proposed to guarantee that the kind of GRNs under consideration here has a unique nonnegative equilibrium point which is globally asymptotically stable. The M-matrix-based stability criteria derived here can be easily verified, since they are to check whether a constant matrix is a nonsingular M-matrix. Several numerical examples are offered to illustrate the effectiveness of the approach proposed in this paper.