Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses
In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.
[1] Kosto B. Neural networks and fuzzy systems-a dynamical system approach
to machine intelligence. Englewood Cliffs (NJ):Prentice-Hall; 1992. p.
38-108.
[2] Kosto B. Bi-directional associative memories. IEEE Trans Syst Man
Cybernet 1988;18:49-60.
[3] Kosto B. Adaptive bi-directional associative memories. Appl Opt
1987;26:4947-4960.
[4] Kohonen T. Self-organization and associative memory. New York:
Springer; 1988.
[5] Cao J. Periodic oscillatory solution of bidirectional associative memory
networks with delays. Phys Rev E 2000;61:1825-1828.
[6] Cao J, Wang L. Exponential stability and periodic oscillatory solution in
BAM networks with delays. IEEE Trans Neural Networks 2002;13(2):457-
463.
[7] Cao J. Global asymptotic stability of delayed bi-directional associative
memory neural networks. Appl Math Computer 2003;142:333-339.
[8] Cao J, J.L. Liang, J. Lam, Exponential stability of high-order bidirectional
associative memory neural networks with time delays, Physical D 199
(2004) 425-436.
[9] J. Cao, D. Ho, X. Huang, LMI-based criteria for global robust stability
of bidirectional associative memory networks with time delay, Nonlinear
Anal. 66 (2007) 1558-1572.
[10] Liao XF, Yu JB. Qualitative analysis of bidirectional associative memory
with time delays. Int J Circuit Theory Appl 1998;26:219-229.
[11] Gopalsamy K, He XZ. Delay-independent stability in bi-directional
associative memory networks. IEEE Trans Neural Networks 1994;5:998-
1002.
[12] Liang XB. Global exponential stability and application of the Hopfield
neural networks. Sci China 1995;25(5):523-532.
[13] Wei JJ, Ruan SG. Stability and bifurcation in a neural network model
with two delays. Physical D 1999;130:255-272.
[14] Jin C. Stability analysis of discrete-time Hopfeld BAM neural networks.
Acta Auto Silica 1999;25(5):606-612.
[15] Xia YH, Cao J, Lin M. New results on the existence and uniqueness
of almost periodic solutions for BAM neural networks with continuously
distributed delays. Chaos, Solitons & Fractals 2007;314:928-936.
[16] Cao J. Global stability analysis in delayed cellular neural networks.
Phys Rev E 1999;59:5940-5944.
[17] Cao J, Chen A, Huang X. Almost periodic attractor of delayed neural
networks with variable coeffcients. Phys Lett A 2005;340:104-120.
[18] Kelly DG. Stability in contractive nonlinear neural networks. IEEE
Trans Biomed Eng 1990;37:231-242.
[19] Huang X, Cao J. Almost periodic solutions of inhibitory cellular neural
networks with time-vary delays. Phys Lett A 2003;314:222-231.
[20] Chen A, Cao J. Existence and attractivity of almost periodic solutions
for cellular networks with distributed delays and variable coefficients.
Appl Math Comp 2003;134:125-140.
[21] Xia YH, Cao J. Almost periodicity in an ecological mode with Mpredators
and N-preys by -pure-delay type- system. Nonlinear Dyn
2005;39(3):275-304.
[22] Xia YH, Cao J. Global attractivity of a periodic ecological model with
m-predators and n-preys by -pure-delay type- system. Comput Appl Math
[to appear].
[23] S. Arik, V. Tavsanoglu, Global asymptotic stability analysis of bidirectional
associative memory neural networks with constant time delays,
Neurocomputing 68 (2005) 161-171.
[24] Haibo Gu, Haijun Jiang, Zhidong Teng ,Existence and globally exponential
stability of periodic solution of BAM neural networks with impulses
and recent-history distributed delays, Neurocomputing 71 (2008) 813-
822.
[25] Yonghui Xia , Zhenkun Huang , Maoan Han. Existence and globally exponential
stability of equilibrium for BAM neural networks with impulses
Chaos, Solitons and Fractals 37 (2008) 588-597
[1] Kosto B. Neural networks and fuzzy systems-a dynamical system approach
to machine intelligence. Englewood Cliffs (NJ):Prentice-Hall; 1992. p.
38-108.
[2] Kosto B. Bi-directional associative memories. IEEE Trans Syst Man
Cybernet 1988;18:49-60.
[3] Kosto B. Adaptive bi-directional associative memories. Appl Opt
1987;26:4947-4960.
[4] Kohonen T. Self-organization and associative memory. New York:
Springer; 1988.
[5] Cao J. Periodic oscillatory solution of bidirectional associative memory
networks with delays. Phys Rev E 2000;61:1825-1828.
[6] Cao J, Wang L. Exponential stability and periodic oscillatory solution in
BAM networks with delays. IEEE Trans Neural Networks 2002;13(2):457-
463.
[7] Cao J. Global asymptotic stability of delayed bi-directional associative
memory neural networks. Appl Math Computer 2003;142:333-339.
[8] Cao J, J.L. Liang, J. Lam, Exponential stability of high-order bidirectional
associative memory neural networks with time delays, Physical D 199
(2004) 425-436.
[9] J. Cao, D. Ho, X. Huang, LMI-based criteria for global robust stability
of bidirectional associative memory networks with time delay, Nonlinear
Anal. 66 (2007) 1558-1572.
[10] Liao XF, Yu JB. Qualitative analysis of bidirectional associative memory
with time delays. Int J Circuit Theory Appl 1998;26:219-229.
[11] Gopalsamy K, He XZ. Delay-independent stability in bi-directional
associative memory networks. IEEE Trans Neural Networks 1994;5:998-
1002.
[12] Liang XB. Global exponential stability and application of the Hopfield
neural networks. Sci China 1995;25(5):523-532.
[13] Wei JJ, Ruan SG. Stability and bifurcation in a neural network model
with two delays. Physical D 1999;130:255-272.
[14] Jin C. Stability analysis of discrete-time Hopfeld BAM neural networks.
Acta Auto Silica 1999;25(5):606-612.
[15] Xia YH, Cao J, Lin M. New results on the existence and uniqueness
of almost periodic solutions for BAM neural networks with continuously
distributed delays. Chaos, Solitons & Fractals 2007;314:928-936.
[16] Cao J. Global stability analysis in delayed cellular neural networks.
Phys Rev E 1999;59:5940-5944.
[17] Cao J, Chen A, Huang X. Almost periodic attractor of delayed neural
networks with variable coeffcients. Phys Lett A 2005;340:104-120.
[18] Kelly DG. Stability in contractive nonlinear neural networks. IEEE
Trans Biomed Eng 1990;37:231-242.
[19] Huang X, Cao J. Almost periodic solutions of inhibitory cellular neural
networks with time-vary delays. Phys Lett A 2003;314:222-231.
[20] Chen A, Cao J. Existence and attractivity of almost periodic solutions
for cellular networks with distributed delays and variable coefficients.
Appl Math Comp 2003;134:125-140.
[21] Xia YH, Cao J. Almost periodicity in an ecological mode with Mpredators
and N-preys by -pure-delay type- system. Nonlinear Dyn
2005;39(3):275-304.
[22] Xia YH, Cao J. Global attractivity of a periodic ecological model with
m-predators and n-preys by -pure-delay type- system. Comput Appl Math
[to appear].
[23] S. Arik, V. Tavsanoglu, Global asymptotic stability analysis of bidirectional
associative memory neural networks with constant time delays,
Neurocomputing 68 (2005) 161-171.
[24] Haibo Gu, Haijun Jiang, Zhidong Teng ,Existence and globally exponential
stability of periodic solution of BAM neural networks with impulses
and recent-history distributed delays, Neurocomputing 71 (2008) 813-
822.
[25] Yonghui Xia , Zhenkun Huang , Maoan Han. Existence and globally exponential
stability of equilibrium for BAM neural networks with impulses
Chaos, Solitons and Fractals 37 (2008) 588-597
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62533", author = "Xiaomei Wang and Shouming Zhong", title = "Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses", abstract = "In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.
", keywords = "Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.", volume = "4", number = "1", pages = "146-6", }
