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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 746241, 12 pages
Global -Stability Analysis for Impulsive Stochastic Neural Networks with Unbounded Mixed Delays
1School of Mathematical Sciences, University of Jinan, Jinan 250022, China
2Computer Department, Jinan Vocational College, Jinan 250103, China
Received 19 October 2012; Accepted 14 December 2012
Academic Editor: Chuandong Li
Copyright © 2013 Lizi Yin and Xinchun Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. J. Hopfield and D. W. Tank, “‘Neural’ computation of decisions in optimization problems,” Biological Cybernetics, vol. 52, no. 3, pp. 141–152, 1985.
- J. J. Hopfield and D. W. Tank, “Computing with neural circuits: a model,” Science, vol. 233, no. 4764, pp. 625–633, 1986.
- Z. Wang, Y. Liu, K. Fraser, and X. Liu, “Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays,” Physics Letters A, vol. 354, no. 4, pp. 288–297, 2006.
- S. Blythe, X. Mao, and X. Liao, “Stability of stochastic delay neural networks,” Journal of the Franklin Institute, vol. 338, no. 4, pp. 481–495, 2001.
- C. Huang, Y. He, and H. Wang, “Mean square exponential stability of stochastic recurrent neural networks with time-varying delays,” Computers & Mathematics with Applications, vol. 56, no. 7, pp. 1773–1778, 2008.
- Z. Wang, Y. Liu, M. Li, and X. Liu, “Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 17, no. 3, pp. 814–820, 2006.
- W. Su and Y. Chen, “Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 520–528, 2009.
- L. Wan and Q. Zhou, “Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays,” Applied Mathematics and Computation, vol. 206, no. 2, pp. 818–824, 2008.
- S. Mohamad, K. Gopalsamy, and H. Akça, “Exponential stability of artificial neural networks with distributed delays and large impulses,” Nonlinear Analysis: Real World Applications, vol. 9, no. 3, pp. 872–888, 2008.
- J. Zhou, L. Xiang, and Z. Liu, “Synchronization in complex delayed dynamical networks with impulsive effects,” Physica A, vol. 384, no. 2, pp. 684–692, 2007.
- H. Gu, H. Jiang, and Z. Teng, “Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays,” Neurocomputing, vol. 71, no. 4–6, pp. 813–822, 2008.
- H. Zhang, M. Dong, Y. Wang, and N. Sun, “Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping,” Neurocomputing, vol. 73, no. 13–15, pp. 2689–2695, 2010.
- L. Chen, R. Wu, and D. Pan, “Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays,” Expert Systems with Applications, vol. 38, no. 5, pp. 6294–6299, 2011.
- R. Rakkiyappan, P. Balasubramaniam, and S. Lakshmanan, “Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays,” Physics Letters A, vol. 372, no. 32, pp. 5290–5298, 2008.
- W. Zhou and M. Li, “Mixed time-delays dependent exponential stability for uncertain stochastic high-order neural networks,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 503–513, 2009.
- H. Li, C. Wang, P. Shi, and H. Gao, “New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays,” Neurocomputing, vol. 73, no. 16-18, pp. 3291–3299, 2010.
- O. M. Kwon, S. M. Lee, and J. H. Park, “Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays,” Physics Letters A, vol. 374, no. 10, pp. 1232–1241, 2010.
- Z. Wang, Y. Liu, X. Liu, and Y. Shi, “Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays,” Neurocomputing, vol. 74, no. 1-3, pp. 256–264, 2010.
- C. Li, J. Shi, and J. Sun, “Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks,” Nonlinear Analysis, Theory, Methods and Applications, vol. 74, no. 10, pp. 3099–3111, 2011.
- P. Balasubramaniam and M. S. Ali, “Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays,” Fuzzy Sets and Systems, vol. 161, no. 4, pp. 608–618, 2010.
- X. Liao and C. Li, “An LMI approach to asymptotical stability of multi-delayed neural networks,” Physica D, vol. 200, no. 1-2, pp. 139–155, 2005.
- X. Y. Lou and B. Cui, “New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks,” Neurocomputing, vol. 69, no. 16-18, pp. 2374–2378, 2006.
- Q. Zhang and X. W. J. Xu, “Delay-dependent global stability results for delayed Hopfield neural networks,” Chaos, Solitons and Fractals, vol. 34, no. 2, pp. 662–668, 2007.
- R. Raja, R. Sakthivel, and S. M. Anthoni, “Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects,” Canadian Journal of Physics, vol. 88, no. 12, pp. 885–898, 2010.
- R. Sakthivel, R. Samidurai, and S. M. Anthoni, “New exponential stability criteria for stochastic BAM neural networks with impulses,” Physica Scripta, vol. 82, no. 4, Article ID 045802, 2010.
- R. Sakthivel, R. Samidurai, and S. M. Anthoni, “Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects,” Journal of Optimization Theory and Applications, vol. 147, no. 3, pp. 583–596, 2010.
- S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, vol. 269 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 2001.
- V. B. Kolmanovskiĭ and V. R. Nosov, Stability of Functional-Differential Equations, vol. 180 of Mathematics in Science and Engineering, Academic Press, London, UK, 1986.
- T. Chen and L. Wang, “Global μ-stability of delayed neural networks with unbounded time-varying delays,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1836–1840, 2007.
- X. Liu and T. Chen, “Robust μ-stability for uncertain stochastic neural networks with unbounded time-varying delays,” Physica A, vol. 387, no. 12, pp. 2952–2962, 2008.
- J. Cao, K. Yuan, and H. X. Li, “Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays,” IEEE Transactions on Neural Networks, vol. 17, no. 6, pp. 1646–1651, 2006.
- S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994.