Abstract and Applied Analysis
Volume 2014 (2014), Article ID 560861, 12 pages
http://dx.doi.org/10.1155/2014/560861
Research Article
Robust Stability Analysis of Neutral-Type Hybrid Bidirectional Associative Memory Neural Networks with Time-Varying Delays
1College of Automation, Chongqing University, Chongqing 400044, China
2Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China
3School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1
Received 5 March 2014; Accepted 2 May 2014; Published 27 May 2014
Academic Editor: Gani Stamov
Copyright © 2014 Wei Feng et al. 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.
Linked References
- L. O. Chua, CNN: A Paradigm for Complexity, World Scientific Publishing, River Edge, NJ, USA, 1998.
- Y. Fang and T. G. Kincaid, “Stability analysis of dynamical neural networks,” IEEE Transactions on Neural Networks, vol. 7, no. 4, pp. 996–1006.
- A. N. Michel and D. Liu, Qualitative Analysis and Synthesis of Recurrent Neural Networks, CRC Press, New York, NY, USA, 2001. View at MathSciNet
- B. Kosko, “Adaptive bidirectional associative memories,” Applied Optics, vol. 26, no. 23, pp. 4947–4960, 1987. View at Google Scholar · View at Scopus
- B. Kosko, “Bidirectional associative memories,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 49–60, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
- M. S. Mahmoud and Y. Xia, “LMI-based exponential stability criterion for bidirectional associative memory neural networks,” Neurocomputing, vol. 74, no. 1–3, pp. 284–290, 2010. View at Publisher · View at Google Scholar · View at Scopus
- H. Wang, Q. Song, and C. Duan, “LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions,” Mathematics and Computers in Simulation, vol. 81, no. 4, pp. 837–850, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- Z. Zhang and D. Zhou, “Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks,” Journal of the Franklin Institute, vol. 347, no. 5, pp. 763–780, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- P. Balasubramaniam and M. S. Ali, “Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays,” Mathematical and Computer Modelling, vol. 53, no. 1-2, pp. 151–160, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- Z. Luo, J. Li, and J. Shen, “Stability of bidirectional associative memory networks with impulses,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 1658–1667, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- R. Raja and S. M. Anthoni, “Global exponential stability of BAM neural networks with time-varying delays: the discrete-time case,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 613–622, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- Z. Zhang and K. Liu, “Existence and global exponential stability of a periodic solution to interval general bidirectional associative memory (BAM) neural networks with multiple delays on time scales,” Neural Networks, vol. 24, no. 5, pp. 427–439, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- Q. Zhu, X. Li, and X. Yang, “Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6078–6091, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- Y. Huang, H. Zhang, and Z. Wang, “Multistability and multiperiodicity of delayed bidirectional associative memory neural networks with discontinuous activation functions,” Applied Mathematics and Computation, vol. 219, no. 3, pp. 899–910, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- B. Liu, “Global exponential stability for BAM neural networks with time-varying delays in the leakage terms,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 559–566, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Z. Zhao, F. Liu, X. Xie, X. Liu, and Z. Tang, “Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach,” Neurocomputing, vol. 117, pp. 40–46.
- A. Zhang, J. Qiu, and J. She, “Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks,” Neural Networks, vol. 50, pp. 98–109.
- Z. Zhang, K. Liu, and Y. Yang, “New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type,” Neurocomputing, vol. 81, pp. 24–32, 2012. View at Publisher · View at Google Scholar · View at Scopus
- Q. Song and J. Cao, “Dynamics of bidirectional associative memory networks with distributed delays and reaction-diffusion terms,” Nonlinear Analysis: Real World Applications, vol. 8, no. 1, pp. 345–361, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- X. Liao and K.-W. Wong, “Robust stability of interval bidirectional associative memory neural network with time delays,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 34, no. 2, pp. 1142–1154, 2004. View at Publisher · View at Google Scholar · View at Scopus
- X. Lou and B. Cui, “On the global robust asymptotic stability of BAM neural networks with time-varying delays,” Neurocomputing, vol. 70, no. 1–3, pp. 273–279, 2006. View at Publisher · View at Google Scholar · View at Scopus
- J. H. Park, “Robust stability of bidirectional associative memory neural networks with time delays,” Physics Letters A: General, Atomic and Solid State Physics, vol. 349, no. 6, pp. 494–499, 2006. View at Publisher · View at Google Scholar · View at Scopus
- S. Senan and S. Arik, “Global robust stability of bidirectional associative memory neural networks with multiple time delays,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 37, no. 5, pp. 1375–1381, 2007. View at Publisher · View at Google Scholar · View at Scopus
- M. Gao and B. Cui, “Global robust exponential stability of discrete-time interval BAM neural networks with time-varying delays,” Applied Mathematical Modelling, vol. 33, no. 3, pp. 1270–1284, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- S. Senan and S. Arik, “New results for global robust stability of bidirectional associative memory neural networks with multiple time delays,” Chaos, Solitons & Fractals, vol. 41, no. 4, pp. 2106–2114, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- L. Sheng and H. Yang, “Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays,” Chaos, Solitons & Fractals, vol. 40, no. 5, pp. 2102–2113, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- M. S. Ali and P. Balasubramaniam, “Robust stability of uncertain fuzzy Cohen-Grossberg BAM neural networks with time-varying delays,” Expert Systems with Applications, vol. 36, no. 7, pp. 10583–10588, 2009. View at Publisher · View at Google Scholar · View at Scopus
- Y. Yuan and X. Li, “New results for global robust asymptotic stability of BAM neural networks with time-varying delays,” Neurocomputing, vol. 74, no. 1–3, pp. 337–342, 2010. View at Publisher · View at Google Scholar · View at Scopus
- Q. Zhou and L. Wan, “Global robust asymptotic stability analysis of BAM neural networks with time delay and impulse: an LMI approach,” Applied Mathematics and Computation, vol. 216, no. 5, pp. 1538–1545, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- S. Senan, S. Arik, and D. Liu, “New robust stability results for bidirectional associative memory neural networks with multiple time delays,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11472–11482, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- X. Li and J. Jia, “Global robust stability analysis for BAM neural networks with time-varying delays,” Neurocomputing, vol. 120, pp. 499–503.
- J. Cao, D. W. C. Ho, and X. Huang, “LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 7, pp. 1558–1572, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- J. Qiu and J. Cao, “Delay-dependent robust stability of neutral-type neural networks with time delays,” Journal of Mathematical Control Science and Applications, vol. 1, no. 1, pp. 179–188. View at Zentralblatt MATH
- J.-E. Feng, S. Xu, and Y. Zou, “Delay-dependent stability of neutral type neural networks with distributed delays,” Neurocomputing, vol. 72, no. 10–12, pp. 2576–2580, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- Z. Zhang, W. Liu, and D. Zhou, “Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays,” Neural Networks, vol. 25, no. 1, pp. 94–105, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- J. H. Park, C. H. Park, O. M. Kwon, and S. M. Lee, “A new stability criterion for bidirectional associative memory neural networks of neutral-type,” Applied Mathematics and Computation, vol. 199, no. 2, pp. 716–722, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- J. Liu and G. Zong, “New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type,” Neurocomputing, vol. 72, no. 10–12, pp. 2549–2555, 2009. View at Publisher · View at Google Scholar · View at Scopus
- N. Ozcan and S. Arik, “A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3312–3320, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- O. Faydasicok and S. Arik, “A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks,” Neural Networks, vol. 44, pp. 67–71.
- J. Cao, D.-S. Huang, and Y. Qu, “Global robust stability of delayed recurrent neural networks,” Chaos, Solitons & Fractals, vol. 23, no. 1, pp. 221–229, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- T. Ensari and S. Arik, “New results for robust stability of dynamical neural networks with discrete time delays,” Expert Systems with Applications, vol. 37, no. 8, pp. 5925–5930, 2010. View at Publisher · View at Google Scholar · View at Scopus
- V. Singh, “Global robust stability of delayed neural networks: estimating upper limit of norm of delayed connection weight matrix,” Chaos, Solitons & Fractals, vol. 32, no. 1, pp. 259–263, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus