Exponential stability of numerical solutions to stochastic delay Hopfield neural networks

The main aim of this paper is to investigate the exponential stability of the Euler method and the semi-implicit Euler method for stochastic delay Hopfield neural networks. The definition of MS-stability and GMS-stability of these two numerical methods is introduced. Under the conditions which guarantee the stability of the analytical solution, the Euler scheme is proved to be MS-stable and the semi-implicit scheme is to be MS-stable and GMS-stable. An example is given for illustration.

[1]  Li Ronghua,et al.  Exponential stability of numerical solutions to SDDEs with Markovian switching , 2006 .

[2]  Wanrong Cao,et al.  MS-stability of the Euler-Maruyama method for stochastic differential delay equations , 2004, Appl. Math. Comput..

[3]  Mingzhu Liu,et al.  Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation , 2004 .

[4]  Qinghua Zhou,et al.  Exponential stability of stochastic delayed Hopfield neural networks , 2008, Appl. Math. Comput..

[5]  Jian-an Fang,et al.  Global stability of stochastic high-order neural networks with discrete and distributed delays , 2008 .

[6]  E. Platen,et al.  Strong discrete time approximation of stochastic differential equations with time delay , 2000 .

[7]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[8]  Evelyn Buckwar,et al.  Introduction to the numerical analysis of stochastic delay differential equations , 2000 .

[9]  Ronghua Li,et al.  Convergence and stability of numerical solutions to SDDEs with Markovian switching , 2006, Appl. Math. Comput..

[10]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[11]  X. Mao,et al.  Numerical solutions of stochastic differential delay equations under local Lipschitz condition , 2003 .

[12]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .

[13]  Yonghui Sun,et al.  pth moment exponential stability of stochastic recurrent neural networks with time-varying delays , 2007 .