Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (3): 400-404.
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Abstract:
paper we investigate the exponential stability of Hopfield-type stochastic neural networks with variable delays, By using the Razumikhin theorems and Lyapunov functions, we present two types of criteria for the exponential stability in the mean square and almost surely exponential stability of Hopfield-type neural networks. One type involves delay dependent results while the other type involves delay independent results.
Key words: Ｎｅｕｒａｌｎｅｔｗｏｒｋ, Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙ, Ｒａｚｕｍｉｋｈｉｎｔｈｅｏｒｅｍ, Ｌｙａｐｕｎｏｖｆｕｎｃｔｉｏｎ
Shen Yi Zhao Yong Liao Xiaoxin Yang Shuzi. Exponential Stability of Hopfield-Type Stochastic Neural Networks with Variable Delays [J].Acta mathematica scientia,Series A, 2000, 20(3): 400-404.
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http://121.43.60.238/sxwlxbA/EN/Y2000/V20/I3/400
１ ＨｏｐｆｉｅｌｄＪ．Ｎｅｕｒｏｎｓｗｉｔｈｇｒａｄｅｄｒｅｓｐｏｎｓｅｈａｖｅｃｏｌｌｅｃｔｉｖｅｃｏｍｐｕｔａｔｉｏｎａｌｐｒｏｐｅｒｔｉｅｓｌｉｋｅｔｈｏｓｅｏｆｔｗｏｓｔａｔｅｎｅｕｒｏｎｓ．ｉｎＰｒｏｃＮａｔＡｃａｄＳｃｉ，ＵＳＡ，１９８４，８１：３０８８－３０９２ ２ ＦｏｒｔｉＭ，ＴｅｓｉＡ．Ｎｅｗｃｏｎｄｉｔｉｏｎｓｆｏｒｇｌｏｂａｌｓｔａｂｉｌｉｔｙｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈａｐｐｌｉｃａｔｉｏｎｔｏｌｉｎｅａｒａｎｄｑｕａｄｒａｔｉｃｐｒｏｇｒａｍｍｉｎｇｐｒｏｂｌｅｍｓ．ＩＥＥＥＴｒａｎｓＣｉｒｃｕｉｔｓＳｙｓｔＩ，１９９５，４２（７）：３５４－３６６ ３ 梁学斌，吴立德．关于Ｈｏｐｆｉｅｌｄ 型神经网络的全局指数稳定性．科学通报，１９９６，４１（１５）：１４３４－１４３８ ４ ＦｏｒｔｉＭ，ＭａｎｅｔｔｉＳ，ＭａｒｉｎｉＭ．Ａｃｏｎｄｉｔｉｏｎｆｏｒｇｌｏｂａｌｃｏｎｖｅｒｇｅｎｃｅｏｆａｃｌａｓｓｏｆｓｙｍｍｅｔｒｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＩＥＥＥ ＴｒａｎｓＣｉｒｃｕｉｔｓＳｙｓｔＩ，１９９２，３９（６）：４８０－４８３ ５ 梁学斌，吴立德．Ｈｏｐｆｉｅｌｄ 型神经网络的全局指数收敛性．中国科学（Ａ 辑），１９９５，２５（５）：５２３－５３３ ６ 廖晓昕．Ｈｏｐｆｉｅｌｄ型神经网络的稳定性．中国科学（Ａ 辑），１９９３，２３（１０）：１０２５－１０３５ ７ ＭａｔｓｕｏｋａＫ．Ｓｔａｂｉｌｉｔｙｃｏｎｄｉｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｃｏｎｔｉｎｕｏｕｓｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈａｓｙｍｅｔｒｉｃｃｏｎｎｅｃｔｉｏｎｗｅｉｇｈｔｓ．ＮｅｕｒａｌＮｅｔｗｏｒｋｓ，１９９２，５：４９５－５００ ８ ＹａｎｇＨ，ＤｉｌｌｏｎＴＳ．ＥｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙａｎｄｏｓｃｉｌｌａｔｉｏｎｏｆＨｏｐｆｉｅｌｄｇｒａｄｅｄｒｅｓｐｏｎｓｅｎｅｕｒａｌｎｅｔｗｏｒｋ．ＩＥＥＥ ＴｒａｎｓＮｅｕｒａｌＮｅｔｗｏｒｋｓ，１９９４，５（５）：７１９－７２９ ９ ＬｉａｏＸＸ，ＭａｏＸ．Ｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓ．Ｎｅｕｒａｌ，Ｐａｒａｌｌｅｌ＆ ＳｃｉｅｎｔｉｆｉｃＣｏｍｐｕｔａｔｉｏｎｓ，１９９６，４：２０５－２２４ １０ ＬｉａｏＸＸ ，ＭａｏＸ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙａｎｄｉｎｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＳｔｏｃｈａｓｔｉｃＡｎａｌｙｓｉｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓ，１９９６，１４（２）：１６５－１８５ １１ ＬｉａｏＸＸ，ＭａｏＸ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｉｎｍｅａｎｓｑｕａｒｅｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈｄｅｌａｙｓ．Ｉｎ１１ｔｈＳｙｍｐｏｓｉｕｍｏｎＳｙｓｔｅｍＩｄｅｎｔｉｆｉｃａｔｉｏｎＪａｐａｎ，１９９７，２：８４１－８４６ １２ 廖晓昕，毛学荣．随机时滞Ｈｏｐｆｉｅｌｄ 神经网络的均方指数稳定性．华中理工大学学报，１９９７，２５（６）：９５－９７ １３ 沈轶，廖晓昕．Ｈｏｐｆｉｅｌｄ型时滞神经网络的指数稳定性．数学物理学报，１９９９，１９（２）：２１１－２１８ １４ 沈轶，廖晓昕．非线性随机时滞系统族的鲁棒稳定性．自动化学报，１９９９，２５（４）：５３９－５４４ １５ ＭａｏＸ．Ｒａｚｕｍｉｋｈｉｎｔｙｐｅｔｈｅｏｒｅｍｓｏｎｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＳｔｏｃｈａｓｔｉｃＰｒｏｃｅｓｓｅｓａｎｄｔｈｅｉｒＡｐｐｌｉｃａｔｉｏｎｓ，１９９６，６５：２３３－２５０ １６ ＭａｏＸ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：ＭａｒｃｅｌＤｅｋｋｅｒ，１９９４ １７ ＭａｏＸ，ＳｈａｈＡ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｄｅｌａｙｅｑｕａｔｉｏｎｓ．ＳｔｏｃｈａｓｔｉｃｓａｎｄＳｔｏｃｈａｓｔｉｃｓＲｅｐｏｒｔｓ，１９９７，６０：１３５－１５３
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