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Ｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙ,"/> Exponential stability of hopfield type stochastic delay neural netuworks

Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 211-218.

• Articles • Previous Articles     Next Articles

Exponential stability of hopfield type stochastic delay neural netuworks

  

  1. (Huazhong University of Science and Technology, Wuhan 430074)
  • Online:1999-05-01 Published:1999-05-01

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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

CLC Number: 

  • 93D
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