Journal of Applied Mathematics

New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses

Chang-Bo Yang, Ting-Zhu Huang, and Jin-Liang Shao

Full-text: Open access

Abstract

By M-matrix theory, inequality techniques, and Lyapunov functional method, certain sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of periodic solution for a new type of high-order BAM neural networks with continuously distributed delays and impulses. These novel conditions extend and improve some previously known results in the literature. Finally, an illustrative example and its numerical simulation are given to show the feasibility and correctness of the derived criteria.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 247046, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807946

Digital Object Identifier
doi:10.1155/2013/247046

Mathematical Reviews number (MathSciNet)
MR3045414

Zentralblatt MATH identifier
1266.92005

Citation

Yang, Chang-Bo; Huang, Ting-Zhu; Shao, Jin-Liang. New Results for Periodic Solution of High-Order BAM Neural Networks with Continuously Distributed Delays and Impulses. J. Appl. Math. 2013 (2013), Article ID 247046, 11 pages. doi:10.1155/2013/247046. https://projecteuclid.org/euclid.jam/1394807946


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References

  • P. Baldi and A. F. Atiya, “How delays affect neural dynamics and learning,” IEEE Transactions on Neural Networks, vol. 5, no. 4, pp. 612–621, 1994.
  • J. Bélair, S. A. Campbell, and P. Van Den Driessche, “Frustration, stability, and delay-induced oscillations in a neural network model,” SIAM Journal on Applied Mathematics, vol. 56, no. 1, pp. 245–255, 1996.
  • X. Liu, “Stability results for impulsive differential systems with applications to population growth models,” Dynamics & Stability of Systems, vol. 9, no. 2, pp. 163–174, 1994.
  • H. Ye, A. N. Michel, and L. Hou, “Stability analysis of systems with impulse effects,” IEEE Transactions on Automatic Control, vol. 43, no. 12, pp. 1719–1723, 1998.
  • K. Gopalsamy and X. Z. He, “Delay-independent stability in bidirectional associative memory networks,” IEEE Transactions on Neural Networks, vol. 5, no. 6, pp. 998–1002, 1994.
  • J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays,” IEEE Transactions on Neural Networks, vol. 13, no. 2, pp. 457–463, 2002.
  • H. Huang and J. Cao, “On global asymptotic stability of recurrent neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 142, no. 1, pp. 143–154, 2003.
  • X. Yang, C. Li, X. Liao, D. J. Evans, and G. M. Megson, “Global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays,” Applied Mathematics and Computation, vol. 171, no. 1, pp. 108–121, 2005.
  • T. Zhou, A. Chen, and Y. Zhou, “Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays,” Physics Letters A, vol. 343, no. 5, pp. 336–350, 2005.
  • J. Shao, T. Huang, and X. Wang, “Improved global robust exponential stability criteria for interval neural networks with time-varying delays,” Expert Systems With Applications, vol. 38, pp. 15587–15593, 2011.
  • S. L. Wu, K. L. Li, and T. Z. Huang, “Exponential stability of static neural networks with time delay and impulses,” IET Control Theory and Applications, vol. 5, no. 8, pp. 943–951, 2011.
  • I. M. Stamova, R. Ilarionov, and R. Vaneva, “Impulsive control for a class of neural networks with bounded and unbounded delays,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 285–290, 2010.
  • J. J. Hopfield and D. W. Tank, “Computing with neural circuits A,” Science, vol. 233, no. 4764, pp. 625–633, 1986.
  • B. Kosko, “Bi-dierctional associative memories,” IEEE Transactions on Systems, Man and Cybernetics, vol. 18, no. 1, pp. 49–60, 1988.
  • Y. T. Li and C. B. Yang, “Global exponential stability analysis on impulsive BAM neural networks with distributed delays,” Journal of Mathematical Analysis and Applications, vol. 324, no. 2, pp. 1125–1139, 2006.
  • Y. Xia, Z. Huang, and M. Han, “Existence and globally exponential stability of equilibrium for BAM neural networks with impulses,” Chaos, Solitons and Fractals, vol. 37, no. 2, pp. 588–597, 2008.
  • K. Li, “Delay-dependent stability analysis for impulsive BAM neural networks with time-varying delays,” Computers and Mathematics with Applications, vol. 56, no. 8, pp. 2088–2099, 2008.
  • Y. T. Li and J. Wang, “An analysis on the global exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses,” Computers and Mathematics with Applications, vol. 56, no. 9, pp. 2256–2267, 2008.
  • Z. Gui, X. S. Yang, and W. Ge, “Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays,” Mathematics and Computers in Simulation, vol. 79, no. 1, pp. 14–29, 2008.
  • H. Gu, H. Jiang, and Z. Teng, “BAM-type impulsive neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3059–3072, 2009.
  • Y. Shao and B. Dai, “The existence of exponential periodic attractor of impulsive BAM neural network with periodic coefficients and distributed delays,” Neurocomputing, vol. 73, no. 16-18, pp. 3123–3131, 2010.
  • X. Li, “Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 292–307, 2009.
  • E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, “High-order neural network structures for identification of dynamical systems,” IEEE Transactions on Neural Networks, vol. 6, no. 2, pp. 422–431, 1995.
  • P. K. Simpson, “Higher-ordered and intraconnected bidirectional associative memories,” IEEE Transactions on Systems, Man and Cybernetics, vol. 20, no. 3, pp. 637–653, 1990.
  • D. W. C. Ho, J. Liang, and J. Lam, “Global exponential stability of impulsive high-order BAM neural networks with time-varying delays,” Neural Networks, vol. 19, no. 10, pp. 1581–1590, 2006.
  • H. Jiang and J. Liu, “Danamics analysis of impulsive stochastic high-order BAM neu ral networks with markovian jumping and mixed delays,” International Journal of Computer Mathematics, vol. 4, pp. 149–170, 2011.
  • H. Gu, “Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays,” Neurocomputing, vol. 74, no. 5, pp. 720–729, 2011.
  • C. Li, C. Li, X. Liao, and T. Huang, “Impulsive effects on stability of high-order BAM neural networks with time delays,” Neurocomputing, vol. 74, no. 10, pp. 1541–1550, 2011.
  • H. F. Huo, W. T. Li, and S. Tang, “Dynamics of high-order BAM neural networks with and without impulses,” Applied Mathematics and Computation, vol. 215, no. 6, pp. 2120–2133, 2009.
  • W. Yang, “Existence and stability of periodic solutions of BAM high-order Hopfield neural networks with impulses and delays on time scales,” Electronic Journal of Differential Equations, vol. 2012, pp. 1–22, 2012.
  • Y. Zhang and Q. G. Wang, “Stationary oscillation for high-order Hopfield neural networks with time delays and impulses,” Journal of Computational and Applied Mathematics, vol. 231, no. 1, pp. 473–477, 2009.