Existence and exponential stability of periodic solutions for a class of Cohen–Grossberg neural networks with bounded and unbounded delays |
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| Affiliation: | 1. Department of Mathematics, Alagappa University, Karaikudi 630 004, India;2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630 004, India;3. School of Mathematics, Southeast University, Nanjing 211189, China;4. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand;5. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Shimane University, Matsue 690–8504, Japan;2. Department of Mathematics, Northeast Forestry University, Harbin 150040, PR China;1. School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China;2. School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510641, PR China;1. University of Carthage, National Institute of Applied Sciences and Technology, Computer Engineering and Mathematics Department, Centre Urbain Nord, BP 676, 1080 Tunis Cedex, Tunisia;2. Mathematical Engineering Laboratory, Tunisia Polytechnic School, University of Carthage, El Khawerzmi street, B.P.743, 2078 La Marsa, Tunisia;3. School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, Shandong, China;1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114 PR China;2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha, Hunan, 410114 PR China |
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| Abstract: | In this paper, a class of Cohen–Grossberg neural networks with bounded and unbounded delays are considered. Without assuming the boundedness, monotonicity, and differentiability of activation functions and any symmetry of interconnections, sufficient conditions for the existence and exponential stability of the periodic solutions are established by using the coincidence degree theorem and differential inequality techniques. The results of this paper are new and they complement previously known results. |
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