Dynamical Behaviors of Stochastic Hopfield Neural Networks with Reaction-Diffusion Terms

Abstract:

Dynamical behaviors of stochastic Hopfield neural network with delays and reaction-diffusion terms are investigated. By employing Lyapunov method, Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness, weak attractor and asymptotic stability are obtained. The criteria are independent of the magnitude of the delays, and dependent on the diffusion effects and the derivative of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

• Periodical: Applied Mechanics and Materials (Volume 432)
• Pages: 523-527
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.432.523
• Online since: September 2013
• Authors: Qing Hua Zhou, Li Wan
• Keywords: Hopfield Neural Networks, Reaction-Diffusion, Ultimate Boundedness

References

[1] J.J. Hopfield: Proceedings of the National Academy of Sciences, USA 79 (1982), 2554.

[2] J.J. Hopfield: Proceedings of the National Academy of Sciences, USA 81 (1984), 3088.

[3] S. Young, P. Scott and N. Nasrabadi: IEEE Transactions on Image Process 6 (1997), 357.

[4] W.J. Li and T. Lee: IEEE Transactions on Neural Networks 12 (2001) , 1400.

[5] L. Liang and J. Cao: Phys. Lett. A 314 (2003), 434.

[6] Z. Zhao, Q. Song and J. Zhang: Comput. Math. Appl. 51 (2006), 475.

[7] K. Li, Z. Li and X. Zhang: Int. Math. Forum 2 (2007), 1397.

[8] R.C. Wu and W. Zhang: Expert Syst. Appl. 36 (2009), 9834.

[9] J. Pan and S. M. Zhong: Neurocomputing 73 (2010), 1344.

[10] X. H. Zhang, S. L. Wu and K. L. Li: Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 1524.

[11] Y. F. Wang, P. Lin and L. S. Wang: Nonlinear Anal-Real. 13 (2012), 1353.

[12] H. Huang and G. Feng: Physica A 381 (2007) , 93.

[13] Q. Song and Z. Wang: Physica A 387 (2008), 3314.

[14] C. Huang, P. Chen, Y. He, L. Huang and W. Tan : Appl. Math. Lett. 21 (2008) , 701.

[15] C. Huang and J.D. Cao: Neurocomputing 72 (2009), 3352.

[16] H.Y. Zhao, N. Ding and L. Chen: Chaos Soliton. Fract. 40 (2009) , 1653.

[17] M. Dong, H. Zhang and Y. Wang,: Neurocomputing 72 (2009), (1999).

[18] C. Huang and J.D. Cao: Neurocomputing 73 (2010), 986.

[19] X.D. Li: Neurocomputing 73 (2010), 7498.

[20] Q. Zhu and J. Cao: IEEE Trans. Syst. Man Cybern. B 41 (2011), 341.

[21] C.H. Wang, Y.G. Kao and G.W. Yang: Neurocomputing 89 (2012), 55.

[22] Y. Xu and B. Cui: Chaos Soliton. Fract. 36 (2008) , 469.

[23] Q. Song and Z. Zhao: Chaos Soliton. Fract. 25 (2005) , 393.

[24] H. Jiang and Z. Teng: Neural Networks 17 (2004), 1415.

[25] H. Jiang and Z. Teng: Neural Networks 72 (2009), 2455.

[26] L. Wan and Q.H. Zhou: Nonlinear Anal-Real 12 (2011), 2561.

[27] L. Wan, Q.H. Zhou, P. Wang and J. Li: Nonlinear Anal-Real 13 (2012), 953.

[28] R. Temam: Infinite Dimensional Dynamical Systems in Mechanics and Physics (Springer, NewYork, 1998).