Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms

Volume 9, Issue 3, pp 1285--1305 http://dx.doi.org/10.22436/jnsa.009.03.52

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1462 Downloads
• 2816 Views

Authors

Changjin Xu - Guizhou Key Laboratory of Economics System Simulation Guizhou, University of Finance and Economics, Guiyang 550004, China. Peiluan Li - School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China.

Abstract

This paper is concerned with the existence and exponential stability of anti-periodic solutions of a neutral BAM neural network with time-varying delays in the leakage terms. Using some analysis skills and Lyapunov method, a series of sufficient conditions for the existence and exponential stability of anti-periodic solutions to the neutral BAM neural networks with time-varying delays in the leakage terms are presented. Our results are new and complement some previously known ones.

Share and Cite

Keywords

• Neutral BAM neural network
• anti-periodic solution
• exponential stability
• time-varying delay
• leakage term.

MSC

•  34C25
•  34K13
•  34K25

References

• [1] M. S. Ali, P. Balasubramaniam, Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays, Chaos Solitons Fractals, 42 (2009), 2191-2199.


• [2] A. P. Chen, L. H. Huang, J. D. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 2003 (137), 177-193.


• [3] Q. Y. Fan, W. T. Wang, X. J. Yi, Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays, J. Comput. Appl. Math., 230 (2009), 762-769.


• [4] S. H. Gong, Anti-periodic solutions for a class of Cohen-Grossberg neural networks, Comput. Math. Appl., 58 (2009), 341-347.


• [5] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Populations Dynamics, Kluwer Academic Publishers, Dordrecht (1992)


• [6] K. Gopalsamy, Leakage delays in BAM, J. Math. Anal. Appl., 325 (2007), 1117-1132.


• [7] S. J. Guo, L. H. Huang, Hopf bifurcating periodic orbits in a ring of neurons with delays, Phys. D, 183 (2003), 19-44.


• [8] S. Haykin, Neural Networks, Prentice-Hall, NJ (1994)


• [9] D. W. C. Ho, J. L. Liang, J. Lam, Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Netw., 19 (2006), 1581-1590.


• [10] Z. D. Huang, L. Q. Peng, M. Xu, Anti-periodic solutions for high-order cellular neural networks with time-varying delays, Electron J. Differ. Equ., 2010 (2010), 9 pages.


• [11] H. J. Jiang, Z. D. Teng, Boundedness, periodic solutions and global stability for cellular neural networks with variable coeficients and infinite delays, Neurocomputing, 72 (2009), 2455-2463.


• [12] B. Kosok, Neural Networks and Fuzzy Systems, Prentice-Hall, NewDelhi (1992)


• [13] S. Lakshmanan, J. H. Park, T. H. Lee, H. Y. Jung, R. Rakkiyappan, Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays, Appl. Math. Comput., 219 (2013), 9408-9423.


• [14] Y. K. Li , Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3326-3336.


• [15] Y. K. Li, X. R. Chen, L. Zhao, Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing, 72 (2009), 1621-1673.


• [16] Y. K. Li, Y. Q. Li, Existence and exponential stability of almost periodic solution for neutral delay BAM neural networks with time-varying delays in leakage terms, J. Frankin Inst., 350 (2013), 2808-2825.


• [17] Y. K. Li, C. Wang, Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses, Fuzzy Sets Syst., 217 (2013), 62-79.


• [18] Y. K. Li, E. L. Xu, T. W. Zhang, Existence and stability of anti-periodic solution for a class of generalized neural networks with impulsives and arbitrary delays on time scales, J. Inequal. Appl., 2010 (2010), 19 pages.


• [19] Y. K. Li, L. Yang, Anti-periodic solutions for Cohen-Grossberg neural netowrks with bounded and unbounded dealys, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3134-3140.


• [20] Y. K. Li, L. Yang, W. Q. Wu, Anti-periodic solutions for a class of Cohen-Grossberg neural networks with time-varying on time scales, Int. J. Syst. Sci., 42 (2011), 1127-1132.


• [21] Y. G. Liu, Z. X. Huang, L. P. Chen, Almost periodic solution of impulsive Hopfield neural networks with finite distributed delays, Neural Comput. Appl., 21 (2012), 821-831.


• [22] D. Y. Liu, W. J.Wu, H. T. Liu, J. W. Zhang, Anti-periodic solutions for interval general Bidirectional Associative Memory (BAM) neural networks with impulses on time scales, J. Infor. Comput. Sci., 8 (2011), 3847-3857.


• [23] C. X. Ou, Anti-periodic solutions for high-order Hopfield neural networks, Comput. Math. Appl., 56 (2008), 1838-1844.


• [24] L. J. Pan, J. D. Cao, Anti-periodic solution for delayed cellular neural networks with impulsive effects, Nonlinear Anal. Real World Appl., 12 (2011), 3014-3027.


• [25] J. H. Park, S. M. Lee, O. M. Kwon, On exponential stability of bidirectional associative memory neural networks with time-varying delays, Chaos Solitons Fractals, 39 (2009), 1083-1091.


• [26] G. Q. Peng, L. H. Huang, Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Nonlinear Anal. Real World Appl., 10 (2009), 2434-2440.


• [27] L. Peng, W. T. Wang, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms, Neurocomputing, 111 (2013), 27-33.


• [28] R. Raja, S. M. Anthoni, Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 613-622.


• [29] R. Sakthivel, A. Arunkumar, K. Mathiyalagan, S. M. Anthoni, Robust passivity analysis of fuzzy Cohen-Grossberg BAM neural networks with time-varying delays, Appl. Math. Comput., 218 (2011), 3799-3809.


• [30] R. Samidurai, R. Sakthivel, S. M. Anthoni, Global asymptotic stability of BAM neural networks mixed delays and impulses, Appl. Math. Comput., 212 (2009), 113-119.


• [31] J. Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Phys. Lett. A, 372 (2008), 5011-5016.


• [32] P. L. Shi, L. Z. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses , Appl. Math. Comput., 216 (2010), 623-630.


• [33] Y. Y. Song, Y. Y. Han, Y. H. Peng, Stability and Hopf bifurcation in an unidirectional ring of n neurons with distributed delays, Neurocomputing, 121 (2013), 442-452.


• [34] Q. K. Song, Z. D. Wang, An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays, Nonlinear Anal. Real World Appl., 8 (2007), 1224-1234.


• [35] X. R. Wei, Z. P. Qiu, Anti-periodic solutions for BAM neural networks with time delays, Appl. Math. Comput., 221 (2013), 221-229.


• [36] A. P. Zhang, Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays, Adv. Difference. Equ., 2013 (2013), 14 pages.


• [37] Z. Q. Zhang, K. Y. 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 Netw., 24 (2011), 427-439.


• [38] Z. Q. Zhang, K. Y. Liu, Y. Yang, New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type, Neurocomputing, 81 (2012), 24-32.


• [39] Z. Q. Zhang, W. B. Liu, D. M. Zhou, Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays, Neural Netw., 25 (2012), 94-105.


• [40] Z. Q. Zhang, Y. Yang, Y. S. Huang, Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays, Neural Netw., 24 (2011), 457-465.


• [41] C. R. Zhang, B. D. Zheng, L. C. Wang, Multiple Hopf bifurcations of symmetric BAM neural network model with delay, Appl. Math. Lett., 22 (2009), 616-622.


• [42] Z. Q. Zhang, D. M. Zhou, Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks, J. Franklin Inst., 347 (2010), 763-780.