Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 211-218.
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Abstract:
In this paper the exponential stability in mean square and almost surely exponential stability are investigated for stochastic neural networks with delay of the form
dx(t)=[-Ax(t)+Bσ(x(t-τ))]dt + f(t,x(t),x(t-τ))dw(t).
For such neural networks, several sufficient conditions for the exponential stability are established by the Lyapunov function method together with martigale inequalities, The obtained results are dependent of the size of delay. Some stability criteria in the literature for the deterministic neural networks with delay x’(t) = -Ax(t)+ Bσ(x(t-τ)) and neural networks x’(t) = -Ax(t) + Bσ(x(t)) are included as special cases.
Key words: Ｓｔｏｃｈａｓｔｉｃｄｅｌａｙｎｅｕｒａｌｎｅｔｗｏｒｋ')">Ｓｔｏｃｈａｓｔｉｃｄｅｌａｙｎｅｕｒａｌｎｅｔｗｏｒｋ, Ｌｙａｐｕｎｏｖｆｕｎｃｔｉｏｎ, Ｍａｒｔｉｇａｌｅｉｎｅｑｕａｌｉｔｙ, Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙ
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Shen Yi, Liao Xiaoxin . Exponential stability of hopfield type stochastic delay neural netuworks[J].Acta mathematica scientia,Series A, 1999, 19(2): 211-218.
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URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I2/211
１ ＨｏｐｆｉｅｌｄＪＪ．Ｎｅｕｒｏｎｓｗｉｔｈｇｒａｄｅｄｒｅｓｐｏｎｓｅｈａｖｅｃｏｌｌｅｃｔｉｖｅｃｏｍｐｕｔａｔｉｏｎａｌｐｒｏｐｅｒｔｉｅｓｌｉｋｅｔｈｏｓｅｏｆｔｗｏｓｔａｔｅｎｅｕｒｏｎｓ．ＩｎＰｒｏｃＮａｔＡｃａｄＳｃｉ，ＵＳＡ，１９８４，８１：３０８８－３０９２ ２ ＦｏｒｔｉＭ，ＭａｎｅｔｔｉＳ，ＭａｒｉｎｉＭ．Ａｃｏｎｄｉｔｉｏｎｆｏｒｇｌｏｂａｌｃｏｎｖｅｒｇｅｎｃｅｏｆａｃｌａｓｓｏｆｓｙｍｍｅｔｒｉｃｎｅｕｒａｌｃｉｒｃｕｉｔｓ．ＩＥＥＥＴｒａｎｓＣｉｒｃｕｉｔｓＳｙｓｔ，１９９２，３９：４８０－４８３ ３ Ｈｉｒｓｃｈ Ｍ Ｗ．Ｃｏｎｖｅｒｇｅｎｔａｃｔｉｖａｔｉｏｎｄｙｎａｍｉｃｓｉｎｃｏｎｔｉｎｕｏｕｓｎｅｔｗｏｒｋｓ．ＮｅｕｒａｌＮｅｔｗｏｒｋｓ，１９８９，２：３３１－３４９ ４ ＭａｔｓｕｏｋａＫ．Ｓｔａｂｉｌｉｔｙｃｏｎｄｉｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｃｏｎｔｉｎｕｏｕｓｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈａｓｙｍｍｅｔｒｉｃｃｏｎｎｅｃｔｉｏｎｗｅｉｇｈｔｓ．ＮｅｕｒａｌＮｅｔｗｏｒｋｓ，１９９２，５：４９５－５００ ５ 廖晓昕．Ｈｏｐｆｉｅｌｄ型神经网络的稳定性．中国科学，Ａ 辑，１９９３，２３：１０２５－１０３５ ６ 梁学斌，吴立德．Ｈｏｐｆｉｅｌｄ型神经网络的全局指数稳定性及应用．中国科学，Ａ 辑，１９９５，２５：５２３－５３２ ７ 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，１９９６，４１：１４３４－１４３８ ８ ＹａｎｇＨ，ＤｉｌｌｉｏｎＴＳ．ＥｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙａｎｄｏｓｃｉｌｌａｔｉｏｎｏｆＨｏｐｆｉｅｌｄｇｒａｄｅｄｒｅｓｐｏｎｓｅｎｅｕｒａｌｎｅｔｗｏｒｋ．ＩＥＥＥ ＴｒａｎｓＮｅｕｒａｌＮｅｔｗｏｒｋｓ，１９９４，５：７１９－７２９ ９ ＦａｎｇＹ，ＫｉｎｃａｉｄＴ Ｇ．Ｓｔａｂｉｌｉｔｙａｎａｌｙｓｉｓｏｆｄｙｎａｍｉｃａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＩＥＥＥ ＴｒａｎｓＮｅｕｒａｌＮｅｔｗｏｒｋ，１９９６，７：９９６－１００６ １０ ＦｏｒｔｉＭ，ＴｃｓｉＡ．Ｎｅｗｃｏｎｄｉｔｉｏｎｓｆｏｒｇｌｏｂａｌｓｔａｂｉｌｉｔｙｏｆｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈａｐｐｌｉｃａｔｉｏｎｔｏｌｉｎｅａｒａｎｄｑｕａ犱ｒａｔｉｃｐｒｏｇｒａｍｍｉｎｇｐｒｏｂｌｅｍｓ．ＩＥＥＥＴｒａｎｓＣｉｒｃｕｉｔｓＳｙｓｔ，１９９５，４２：３５４－３６６ １１ ＺｈａｎｇＹ．ＧｌｏｂａｌｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙａｎｄｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｏｆｄｅｌａｙＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＩｎｔｅｒｎａｔｉｏｎａｌＪｏｕｒｎａｌｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ．１９９６，２７：２２７－２３１ １２ ＣａｏＹＪ，ＷｕＱ Ｈ．Ａｎｏｔｅｓｔａｂｉｌｉｔｙｏｆａｎａｌｏｇｎｅｕｒａｌｎｅｔｗｏｒｋｗｉｔｈｔｉｍｅｄｅｌａｙｓ．ＩＥＥＥＴｒａｎｓＮｅｕｒａｌＮｅｔｗｏｒｋ，１９９６，７：１５３３－１５３５ １３ ＧｏｐａｌｓａｍｙＫ，ＨｅＸＸ．ＳｔａｂｉｌｉｔｙｉｎａｓｙｍｍｅｔｒｉｃＨｏｐｆｉｅｌｄｎｅｔｓｗｉｔｈｔｒａｎｓｍｉｓｓｉｏｎｄｅｌａｙｓ．ＰｈｙｓｉｃａＤ，１９９４，７６：３４４－３５８ １４ 李宏伟．时滞神经网络的稳定性与振动．西安交通大学博士论文，１９９６ １５ ＹｅＨ，ＭｉｃｈｅｌＡ Ｎ，ＷａｎｇＫ．Ｒｏｂｕｓｔｓｔａｂｉｌｉｔｙｏｆｎｏｎｌｉｎｅａｒｔｉｍｅｄｅｌａｙｓｙｓｔｅｍｓｗｉｔｈａｐｐｌｉｃａｔｉｏｎｓｔｏｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＩＥＥＥＴｒａｎｓＣｉｒｃｕｉｔｓＳｙｓｔ，１９９６，４３：５３２－５４３ １６ ＬｉａｏＸＸ，ＭａｏＸ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙａｎｄｉｎｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＳｔｏｃｈａｓｔｉｃＡｎａｌｙｓｉｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓ，１９９６，１４：１６５－１８５ １７ ＬｉａｏＸＸ，ＭａｏＸ．Ｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓ．ＮｃｕｒａｌＰａｒａｌｌｃｌ＆ ＳｃｌｅｎｔｉｆｉｃＣｏｍｐｕｔａｔｉｏｎ，１９９６，４：２０５－２２４ １８ ＬｉａｏＸ Ｘ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｉｎ ｍｅａｎｓｑｕａｒｅｏｆｓｔｏｃｈａｓｔｉｃｎｅｕｒａｌｎｅｔｗｏｒｋｓｗｉｔｈｄｅｌａｙｓ．１１ｔｈＩＦＡＣＳｙｍｐｏｓｉｕｍＳｙｓｔｅｍＩｄｅｎｔｉｆｉｃａｔｉｏｎ，１９９７，２：８４１－８４６ １９ ＭａｏＸ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＭａｒｃｅｌＤｅｋｋｅｒ，１９９４ ２０ ＭａｏＸ，ＳｈａｈＡ．Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｄｅｌａｙｅｑｕａｔｉｏｎｓ．ＳｔｏｃｈａｓｔｉｃｓａｎｄＳｔｏｃｈａｓｔｉｃｓＲｅｐｏｒｔｓ１９９７，６０：１３５－１５３
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