Split-Step Backward Euler Method for Stochastic Delay Hopfield Neural Networks with Markovian Switching

Rong Hua Li; Li Yang; Jia Wei Li

doi:10.4028/www.scientific.net/AMM.58-60.1390

Paper Titles

The Study of Moving Images Track Recording System which Based on Mean Shift Algorithm
p.1365

A GA-BP Neural Network Model for Predicting the Temperature of Slabs in the Reheating Furnace
p.1371

Lung Nodule Segmentation Using Mathematical Morphology
p.1378

Angle Constraints for Point Correspondence in Multi-Ocular Vision
p.1384

Split-Step Backward Euler Method for Stochastic Delay Hopfield Neural Networks with Markovian Switching
p.1390

Trajectory Model of J-Type Groove and its Curve Fitting of B-Spline
p.1396

Aircraft Cockpit Distributed Simulation Based on Embedded Ethernet and PoE
p.1402

Bionic Autonomous Learning Mechanism Study Based on Automaton and Applied on Robot
p.1408

Tacit Extraction for Keyword in Chinese
p.1415

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 58-60Split-Step Backward Euler Method for Stochastic...

Split-Step Backward Euler Method for Stochastic Delay Hopfield Neural Networks with Markovian Switching

Abstract:

In this paper, split-step backward Euler method for stochastic delay Hopfield neural networks with Markovian switching is considered. The main aim of this paper is to show that the numerical approximation solution is convergent to the true solution with order. The conditions under which the numerical solution is exponentially stable in mean square are given. An example is provided for illustration.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 58-60)

Pages:

1390-1395

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.58-60.1390

Citation:

Cite this paper

Online since:

June 2011

Authors:

Rong Hua Li, Li Yang, Jia Wei Li

Keywords:

Delay, Markovian Switching, MS-Stability, Split-Step Backward Euler Scheme, Stochastic Hopfield Neural Network

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] H. Liu, L. Zhao, Z. Zhang, Y. Ou, Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays, Neurocomputing 72(2009) 3669-3674.

DOI: 10.1016/j.neucom.2009.07.003

Google Scholar

[2] X. Lou, B, Cui, Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J. Math. Appl. 328(2007) 316-326.

DOI: 10.1016/j.jmaa.2006.05.041

Google Scholar

[3] L. Ronghua,P. Wan-kai, L. Ping-kei, Exponential stability of numerical solutions to stochastic delay Hopfield neural networks, Neurocomputing 73(2010) 920-926.

DOI: 10.1016/j.neucom.2009.09.007

Google Scholar

[4] E. Buckwar, Introduction to the numerical analysis of stochastic delay differential equations, J. Comput. Appl. Math. 125(2000) 297-307.

Google Scholar

[5] U., E. Platen, Strong discrete time approximation of stochastic differential equations with time delay, Math. Comput. Simulation 54(2000) 189-205.

DOI: 10.1016/s0378-4754(00)00224-x

Google Scholar

[6] M. Liu, W. Cao, Z. Fan, Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation, J. Comput. Appl. Math. 170(2004) 255-268.

DOI: 10.1016/j.cam.2004.01.040

Google Scholar

[7] H. Zhang, S. Gan, L. Hu, The split-step backward Euler method for linear stochastic delay differential equations, J. Comput. and Appl. Math. 225 (2009) 558-568.

DOI: 10.1016/j.cam.2008.08.032

Google Scholar

[8] D.J. Higham, X. Mao, A.M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM J. Numer. Anal. 40(2002) 1041-1063.

DOI: 10.1137/s0036142901389530

Google Scholar

[9] X. Mao, Stochastic Differnetial Equations and Applications, Horwood, (1997).

Google Scholar

[10] Q. Zhou, L. Wan, Exponential stability of stochastic delayed Hopfield neural networks, Appl. Math. Comput. 199(2008) 84-89.

DOI: 10.1016/j.amc.2007.09.025

Google Scholar

[11] C. Yuan, X. Mao, Convergence of the Euler- Maruyama method for stochastic differential equations with Markovian switching, Comput. Simulation 64(2004) 223-235.

DOI: 10.1016/j.matcom.2003.09.001

Google Scholar