Global asymptotic stability of a class of nonautonomous integro-differential systems and applications |
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| Institution: | 1. School of Mathematics and Statistics, Key Laboratory for Vegetation Ecology of the Education Ministry, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin 130024, The People''s Republic of China;2. Department of Applied Mathematics, University of Western Ontario, London, Ont., Canada N6A 5B7;1. Politecnico di Milano, Polo Territoriale di Lecco, Via G. Previati 1c, 23900 Lecco, Italy;2. IAPS-INAF– Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere 100, 00133 Roma, Italy;3. CNR-Istituto sull’Inquinamento Atmosferico, via Salaria Km 29,300, 00015 Monterotondo, Roma, Italy;1. Dept. of Math., Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;2. Dept. of Math. and Stats., University of Calgary, Calgary, AB T2N 1N4, Canada;1. Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana - Cuajimalpa, Av. Vasco de Quiroga 4871, Ciudad de México, 05348, Mexico;2. Departamento de Física y Matemáticas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Ciudad de México, 01219, Mexico |
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| Abstract: | In this paper, we study the global asymptotic stability of a class of nonautonomous integro-differential systems. By constructing suitable Lyapunov functionals, we establish new and explicit criteria for the global asymptotic stability in the sense of Definition 2.1. In the autonomous case, we discuss the global asymptotic stability of a unique equilibrium of the system, and in the case of periodic system, we establish sufficient criteria for existence, uniqueness and global asymptotic stability of a periodic solution. Also explored are applications of our main results to some biological and neural network models. The examples show that our criteria are more general and easily applicable, and improve and generalize some existing results. |
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