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Existence and global stability of a periodic solution for a cellular neural network
Institution:1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, Jiangsu, China;2. Key Laboratory of Measurement and Control for Complex System of Ministry of Education, Research Institute of Automation, Southeast University, Nanjing 210096, Jiangsu, China;1. Petroleum Engineering Department, Petroleum University of Technology, Ahwaz, Iran;2. Dynamical Systems & Control (DSC) Research Lab., Electrical Engineering Department, School of Engineering, Persian Gulf University, Boushehr, Iran;3. ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal;1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75918-74934, Iran;2. Faculty of Mathematical Sciences, University of Tabriz, 29 Bahman St., Tabriz 51665-163, Iran;1. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China;2. School of Automation and Electrical Engineering, Tianjin University of Technology and Educations, Tianjin 300222, China;1. Department of Mathematics, Faculty of Mathematics Sciences, Shahid Beheshti University, Tehran, Iran;2. Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran;1. Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, Goiás, Brazil;2. Instituto de Física, Universidade de São Paulo, 05314-970 São Paulo SP, Brazil;3. Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, Paraíba, Brazil
Abstract:Purpose of this study is to investigate the dynamical properties of Chua and Yang cellular neural networks (CNNs). Based on the continuation theorem of coincidence degree theory, a novel sufficient condition with respect to the existence of periodic solution for CNNs is derived. Moreover, a generalized Lyapunov–Krasovskii functional is designed to guarantee the global stability of the existed periodic solution. An illustrative example is given to verify the effectiveness and correctness of the proposed method, furthermore, random disturbance is added in the numerical simulation in order to verify the robustness of the proposed approach.
Keywords:Cellular neural network  Existence  Global stability  Periodic solution  Linear matrix inequality  Lyapunov–Krasovskii functional  Continuation theorem of coincidence degree theory
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