Covergence of stochastic fuzzy Cohen-Grossberg neural networks with reaction-diffusion and distributed delays

In this paper, a class of stochastic fuzzy Cohen-Grossberg neural networks with reaction-diffusion and distributed delays is discussed. Based on Lyapunov functionals, inequality analysis, Ito's formula, nonnegative semimartingale convergence theorem and stochastic analysis, some stability sufficient conditions are presented to guarantee the neural networks to be almost sure and mean square exponentially stable, respectively. The proposed results improve and extend some earlier literature and are easier to verify. For illustration, an example is given to illustrate the feasibility of the results.

[1]  D. He,et al.  Attracting and invariant sets of fuzzy Cohen–Grossberg neural networks with time-varying delays , 2008 .

[2]  Tingwen Huang,et al.  Robust stability of delayed fuzzy Cohen-Grossberg neural networks , 2011, Comput. Math. Appl..

[3]  Tao Yang,et al.  Fuzzy Cellular Neural Network: a new paradigm for image processing , 1997, Int. J. Circuit Theory Appl..

[4]  Jiye Zhang,et al.  Global Exponential Stability of Fuzzy Cohen-Grossberg Neural Networks with Variable Delays , 2007, ISNN.

[5]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[6]  Jinde Cao,et al.  Impulsive Effects on Stability of Fuzzy Cohen–Grossberg Neural Networks With Time-Varying Delays , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Chen An,et al.  The Global Stability of Fuzzy Cellular Neural Networks , 2001 .

[8]  Xiaodi Li,et al.  LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays☆ , 2011 .

[9]  Weifan Zheng,et al.  Stability Analysis of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delays and Reaction-Diffusion Terms , 2010, ISNN.

[10]  Yongkun Li,et al.  Exponential stability of fuzzy Cohen–Grossberg neural networks with time delays and impulsive effects☆ , 2010 .

[11]  Kelin Li,et al.  Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms , 2009 .

[12]  Chun-Mei Yang,et al.  The differences between Cellular Neural Network based and Fuzzy Cellular Nneural Network based mathematical morphological operations , 1998 .

[13]  Tingwen Huang.  Exponential stability of fuzzy cellular neural networks with distributed delay , 2006 .

[14]  A. Friedman.  Stochastic Differential Equations and Applications , 1975 .

[15]  Hongyong Zhao,et al.  Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays , 2009 .

[16]  Xinhua Zhang,et al.  Periodicity of Cohen-Grossberg-type fuzzy neural networks with time-varying delays and impulses , 2010, The 3rd International Conference on Information Sciences and Interaction Sciences.

[17]  Tianping Chen,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions , 2005, Neural Networks.

[18]  Wansheng Tang,et al.  Exponential stability of fuzzy cellular neural networks with constant and time-varying delays , 2004 .

[19]  Simon Haykin,et al.  Neural networks , 1994 .

[20]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

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

[22]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[23]  Qintao Gan,et al.  Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms , 2010, Neural Processing Letters.

[24]  Lili Cui,et al.  Novel criteria on global exponential stability of fuzzy Cohen-Grossberg neural networks with time-varying delay , 2009, 2009 Chinese Control and Decision Conference.

[25]  Aiguo Song,et al.  Robust stability of stochastic Cohen-Grossberg neural networks with mixed time-varying delays , 2009, Neurocomputing.

[26]  Xinzhi Liu,et al.  Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays , 2010, Math. Comput. Model..

[27]  Jinde Cao,et al.  On pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays , 2010, Neurocomputing.

[28]  Manchun Tan.  Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Unbounded Distributed Delays , 2010, Neural Processing Letters.

[29]  Jinde Cao,et al.  Periodic Oscillation of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delay and Variable Coefficients , 2008, J. Appl. Math..

[30]  Ling Chen,et al.  Stability analysis of stochastic fuzzy cellular neural networks with delays , 2008, Neurocomputing.