Global exponential stability of a class of retarded impulsive differential equations with applications |
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| Authors: | Yonghui Xia Patricia J.Y. Wong |
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| Affiliation: | 1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore;1. School of Mathematical Sciences, Capital Normal University, 100048 Beijing, PR China;2. School of Mathematical Sciences, Peking University, 100871 Beijing, PR China;1. Center for Applied Mathematics and Theoretical Physics, and Faculty of Natural Science and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia;2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, People''s Republic of China;3. Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, People''s Republic of China;1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore;1. School of Mathematical Sciences, Capital Normal University, 100048 Beijing, People''s Republic of China;2. School of Mathematical Sciences, Beijing Normal University, 100875 Beijing, People''s Republic of China;3. School of Mathematical Sciences, BCMIIS, Capital Normal University, 100048 Beijing, People''s Republic of China;1. Department of Environmental Health Engineering, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran;2. Center for Water Quality Research (CWQR), Institute for Environmental Research (IER), Tehran University of Medical Sciences, Tehran, Iran;3. Master of Biostatistics, Neyshabur University of Medical Sciences, Neyshabur, Iran;4. Department of Environmental Health Engineering, School of Public Health, Mashhad University of Medical Sciences, Mashhad, Iran;5. Students Research Committee, Neyshabur University of Medical Sciences, Neyshabur, Iran;6. Department of Environmental Health Engineering, Neyshabur University of Medical Sciences, Neyshabur, Iran |
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| Abstract: | This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained. |
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