Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function |
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| Authors: | A Pratap R Raja Jinde Cao G Rajchakit Habib M Fardoun |
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| Institution: | 1. Department of Mathematics, Alagappa University, Karaikudi 630004, India;2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630004, India;3. School of Mathematics, Southeast University, Nanjing 211189, China;4. School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China;5. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand;6. Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia |
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| Abstract: | Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results. |
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| Keywords: | Corresponding author at: School of Mathematics Southeast University Nanjing 211189 China |
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