Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays |
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| Affiliation: | 1. Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Southeast University, Nanjing 210096, China;2. CSN Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210996, Jiangsu, China;2. School of Mathematics and Statistics, and Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Wanzhou 404100, Chongqing, China;3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;1. Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China;2. Department of Mathematics, Southeast University, Nanjing 210096, China;3. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. School of Sciences, Southwest Petroleum University, Chengdu 610050, PR China;2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, PR China;3. College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610050, PR China |
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| Abstract: | A single inertial BAM neural network with time-varying delays and external inputs is concerned in this paper. First, by choosing suitable variable substitution, the original system can be transformed into first-order differential equations. Then, we present several sufficient conditions for the global exponential stability of the equilibrium by using matrix measure and Halanay inequality, these criteria are simple in form and easy to verify in practice. Furthermore, when employing an error-feedback control term to the response neural network, parallel criteria regarding to the exponential synchronization of the drive-response neural network are also generated. Finally, some examples are given to illustrate our theoretical results. |
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| Keywords: | Global exponential stability Global synchronization Matrix measure Inertial BAM neural network Time-varying delays |
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