caa a22 4500 606205756 CHVBK 20210128101008.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00034-015-0006-8 doi (NATIONALLICENCE)springer-10.1007/s00034-015-0006-8 Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms [Elektronische Daten] [Yuanyuan Han, Xian Zhang, Yantao Wang] This paper investigates the asymptotic stability problem for delayed genetic regulatory networks with reaction-diffusion terms under both Dirichlet boundary conditions and Neumann boundary conditions. First, by constructing a new Lyapunov-Krasovskii functional and using Jensen's inequality, Wirtinger's inequality, Green's second identity and the reciprocally convex approach, we establish delay-dependent asymptotic stability criteria that do not require a restriction of the upper bounds of the delays' derivatives being less than 1. Thus, the stability criteria that we establish are less conservative than the existing criteria and extend the range of applications of the theoretical results. In addition, it is shown that the obtained criterion under Dirichlet boundary conditions retains the information about the reaction-diffusion terms, while these do not exist in the criterion under Neumann boundary conditions. It is then theoretically presented that the stability criteria established in this paper are less conservative than the existing ones. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Springer Science+Business Media New York, 2015 Genetic regulatory networks nationallicence Reaction-diffusion terms nationallicence Asymptotic stability nationallicence Time-varying delays nationallicence Han Yuanyuan School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut Zhang Xian School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut Wang Yantao School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/10(2015-10-01), 3161-3190 0278-081X 34:10<3161 2015 34 34 https://doi.org/10.1007/s00034-015-0006-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00034-015-0006-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Han Yuanyuan School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut NATIONALLICENCE 700 1- Zhang Xian School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut NATIONALLICENCE 700 1- Wang Yantao School of Mathematical Science, Heilongjiang University, 150080, Harbin, China aut NATIONALLICENCE 773 0- Circuits, Systems, and Signal Processing Springer US; http://www.springer-ny.com 34/10(2015-10-01), 3161-3190 0278-081X 34:10<3161 2015 34 34