caa a22 4500 606233164 CHVBK 20210128101230.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s10883-014-9230-y doi (NATIONALLICENCE)springer-10.1007/s10883-014-9230-y Belmiloudi Aziz Institut de Recherche MAthématique de Rennes (IRMAR), Université Européenne de Bretagne, 20 avenue Buttes de Coësmes, CS 70839, 35708, Rennes Cédex 7, France aut Dynamical Behavior of Nonlinear Impulsive Abstract Partial Differential Equations on Networks with Multiple Time-Varying Delays and Mixed Boundary Conditions Involving Time-Varying Delays [Elektronische Daten] [Aziz Belmiloudi] Various real-world problems in physics, biology, neuroscience, communication and transport networks, engineering science, and so on, subject to abrupt changes at certain instants during the dynamical processes, can be well-described by impulsive partial differential equations on networks with time-varying delays. The purpose of this paper is to investigate the existence, stability, and global attractivity of a class of coupled impulsive system of nonlinear reaction-diffusion type equations on networks in which different time-varying delays appear both in the nonlinear reaction functions and in the mixed boundary conditions. The problem under consideration can be included coupled systems of reaction-diffusion and ordinary differential equations. By using the method of upper and lower solutions and its associated monotone iterations, the existence-uniqueness of the solution, the stability and attractivity analysis for quasi-monotone nondecreasing and mixed quasi-monotone reaction and impulsive functions, are considered. The results for the general system are applied to the standard PDE reaction-diffusion system without time delays and/or impulsive behavior and to the corresponding ordinary differential system. To illustrate the abstract results, problems of three-species food-chain reaction-diffusion models with time-varying delays and impulsive perturbations are considered. Springer Science+Business Media New York, 2014 Reaction-diffusion systems nationallicence Time-varying delays nationallicence Networks nationallicence Impulsive operators nationallicence Upper-lower solution method nationallicence Asymptotic behavior nationallicence Existence and uniqueness of solution nationallicence Positive solutions nationallicence Biological control nationallicence Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/1(2015-01-01), 95-146 1079-2724 21:1<95 2015 21 10883 https://doi.org/10.1007/s10883-014-9230-y 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/s10883-014-9230-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Belmiloudi Aziz Institut de Recherche MAthématique de Rennes (IRMAR), Université Européenne de Bretagne, 20 avenue Buttes de Coësmes, CS 70839, 35708, Rennes Cédex 7, France aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/1(2015-01-01), 95-146 1079-2724 21:1<95 2015 21 10883