Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 4 (2009), 53 -- 63


Hamid A. Jalab and Rabha W. Ibrahim

Abstract. In this paper, we study the existence and uniqueness solution and investigate the conditions that make it almost-periodic solution for BAM neural networks with retarded delays. The existence of solution established by using Schauder fixed point theorem. The uniqueness established by using Banach fixed point theorem. Moreover we study the parametric stability of such a solution. Also we illustrate our results with an example.

2000 Mathematics Subject Classification: 34K13; 34K14; 92B20.
Keywords: almost-periodicity; BAM neural networks; parametric stability.

Full text


  1. J. Cao and J.Wang, Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Networks, 13(2), (2002).

  2. J. Cao, J. Wang and X.F.Liao, Novel stability criteria of delayed cellular neural networks, Int.J.Neural Systems 13 (2003), 367-375.

  3. J. Cao, D. W. Ho, A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach, Chaos, Solutions and Fractals 24(2005), 1317-1329. MR2123277(2005i:34092). Zbl 1072.92004.

  4. C. Corduneanu, Almost Periodic Functions, 2nd edition, Chelse, New York,1989. Zbl 0672.42008.

  5. A. Chen, L. Huang and J. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, App.Math.and Comp., 137(2003), 177-193. MR1949131(2003k:34127). Zbl 1034.34087.

  6. M. Bahaj, O. Sidki, Almost periodic solutions of semi-linear equations with analytic semigroups in Banach space, Electron. J. Differantial Equations, 98(2002), 1-11. MR1908403(2003b:34155). Zbl 1026.34050.

  7. K. Gopalsamy, X. Z. He, Delay independent stability in bi-directional associative memory networks, IEEE Trans. Neural Networks, 5(1994), 998-1002.

  8. J. J. Hopfield, Neural networks and physical systems with emergent collectiv computational abilities, Proceedings of the National Academy of the Sciences, 79(1982), 2554-2558. MR0652033(83g:92024).

  9. M. Ikeda, Y. Ohata and D. D. Siljak, Parametric stability, in:G.Conte, A.M.Perdo, B.Wyman(Eds.), New Trends in Systems Theory, Birkhauser, Boston (1991), 1-20. MR1125087(92f:93077). Zbl 0736.93001.

  10. C. Jin, Stability analysis of discrete-time Hopfield BAM neural networks, Acta. Auto. Sin., 5(1999), 606-612. MR1751272

  11. B. Kosko, Adaptive bidirectional associative memories, Applied optics, 26 (23) (1987), 4947-4960.

  12. E. Saund, Dimensionality reduction using connection networks, IEEE Trans. On Pattern Analysis and Machine Intelligence, 11(1989), 304-314. Zbl 0678.68089

  13. R. J. Schallkoff, Artificial Intelligence: Engineering Approach, McGraw-Hill, New York, 1990.

  14. V. Sundarapandian, A necessary condition for local asymptotic stability of discrete-time nonlinear systems with parameters, Applied Mathematics Letters 15(2002), 271-274. MR1891545(2003b:93077). Zbl 1016.93057.

  15. V. Sundarapandian, New results on the parametric stability of nonlinear systems, Math. and Comp. Modelling 43 (2006), 9-15. MR2197399(2006m:34130). Zbl pre05023383.

  16. J. J. Wei, S. G. Ruan, Stability and bifurcation in a neural network model with two delays, Phys.D 130(1999), 255-272. MR1692866(2001a:34123). Zbl 1066.34511.

  17. S. Zaidman, Topics in Abstract Differential Equations, in:Pitman Research Notes in Mathematics Ser.II, John Wiley and sons, New York, 1994-1995. MR1327278(96f:34081). Zbl 0806.34001.

Hamid A. Jalab Rabha W. Ibrahim
Department of Computer Science School of Mathematical Sciences
Faculty of Science Faculty of science and Technology
Sana'a University, P.O.Box 14526 Maeen UKM Bangi 43600 Selangor Darul Ehsan
Sana'a,Yemen. Malaysia.
e-mail: e-mail: