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Volumn 48, Issue 4, 2011, Pages 727-747

Existence and global exponential stability of a periodic solution to discrete-time Cohen-Grossberg BAM neural networks with delays

Author keywords

Coincidence degree theory; Global exponential stability; Lyapunov functional; Periodic solutions; Two dimensional discrete time Cohen Grossberg BAM neural networks

Indexed keywords


EID: 79959967095     PISSN: 03049914     EISSN: None     Source Type: Journal    
DOI: 10.4134/JKMS.2011.48.4.727     Document Type: Article
Times cited : (12)

References (45)
  • 1
    • 20444368794 scopus 로고    scopus 로고
    • Global stability analysis of Cohen-Grossberg neural networks with time varying delays
    • S. Arik and Z. Orman, Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Phys. Lett. A 341 (2005), no. 5-6, 410-421.
    • (2005) Phys. Lett. A , vol.341 , Issue.5-6 , pp. 410-421
    • Arik, S.1    Orman, Z.2
  • 2
    • 3442880393 scopus 로고    scopus 로고
    • Boundedness and stability of Cohen-Grossberg neural networks with time-varying delays
    • J. Cao and J. Liang, Boundedness and stability of Cohen-Grossberg neural networks with time-varying delays, J. Math. Anal. Appl. 296 (2004), no. 2, 665-685.
    • (2004) J. Math. Anal. Appl. , vol.296 , Issue.2 , pp. 665-685
    • Cao, J.1    Liang, J.2
  • 3
    • 33947173257 scopus 로고    scopus 로고
    • Periodic bi-directional Cohen-Grossberg neural networks with distributed delays
    • A. P. Chen and J. D. Cao, Periodic bi-directional Cohen-Grossberg neural networks with distributed delays, Nonlinear Anal. 66 (2007), no. 12, 2947-2961.
    • (2007) Nonlinear Anal. , vol.66 , Issue.12 , pp. 2947-2961
    • Chen, A.P.1    Cao, J.D.2
  • 4
    • 70350733462 scopus 로고    scopus 로고
    • Periodic solution to BAM neural network with delays on time scales
    • A. P. Chen and F. L. Chen, Periodic solution to BAM neural network with delays on time scales, Neurocomputing 73 (2009), no. 1-3, 274-282.
    • (2009) Neurocomputing , vol.73 , Issue.1-3 , pp. 274-282
    • Chen, A.P.1    Chen, F.L.2
  • 5
    • 32544432815 scopus 로고    scopus 로고
    • Periodic bidirectional associative memory neural networks with distributed delays
    • A. P. Chen, L. H. Huang, Z. G. Liu, and J. D.Cao, Periodic bidirectional associative memory neural networks with distributed delays J. Math. Anal. Appl. 317 (2006), no. 1, 80-102.
    • (2006) J. Math. Anal. Appl. , vol.317 , Issue.1 , pp. 80-102
    • Chen, A.P.1    Huang, L.H.2    Liu, Z.G.3    Cao, J.D.4
  • 6
    • 0142087577 scopus 로고    scopus 로고
    • Delay-independent stability analysis of Cohen-Grossberg neural networks
    • T. Chen and L. Rong, Delay-independent stability analysis of Cohen-Grossberg neural networks, Phys. Lett. A 317 (2003), no. 5-6, 436-449.
    • (2003) Phys. Lett. A , vol.317 , Issue.5-6 , pp. 436-449
    • Chen, T.1    Rong, L.2
  • 7
    • 67349234534 scopus 로고    scopus 로고
    • Discrete analogue of high-order periodic Cohen-Grossberg neural networks with delays
    • Z. Chen, D. H. Zhao, and X. L. Fu, Discrete analogue of high-order periodic Cohen-Grossberg neural networks with delays, Appl. Math. Comput. 214 (2009), no. 1, 210-217.
    • (2009) Appl. Math. Comput. , vol.214 , Issue.1 , pp. 210-217
    • Chen, Z.1    Zhao, D.H.2    Fu, X.L.3
  • 8
    • 0020970741 scopus 로고
    • Absolute stability and global pattern formation and parallel memory storage by competitive neural networks
    • M. Cohen and S. Grossberg, Absolute stability and global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Systems Man Cybernet. 13 (1983), no. 5, 815-826.
    • (1983) IEEE Trans. Systems Man Cybernet. , vol.13 , Issue.5 , pp. 815-826
    • Cohen, M.1    Grossberg, S.2
  • 9
    • 55949095605 scopus 로고    scopus 로고
    • Global exponential stability of Cohen-Grossberg neural networks with distributed delays
    • B. T. Cui and W. Wu, Global exponential stability of Cohen-Grossberg neural networks with distributed delays, Neurocomputing 72 (2008), no. 1-3, 386-391.
    • (2008) Neurocomputing , vol.72 , Issue.1-3 , pp. 386-391
    • Cui, B.T.1    Wu, W.2
  • 10
    • 55949106693 scopus 로고    scopus 로고
    • New criteria on global robust stability of Cohen-Grossberg neural networks with time varying delays
    • J. Feng and S. Xu, New criteria on global robust stability of Cohen-Grossberg neural networks with time varying delays, Neurocomputing 72 (2008), no. 1-3, 445-457.
    • (2008) Neurocomputing , vol.72 , Issue.1-3 , pp. 445-457
    • Feng, J.1    Xu, S.2
  • 11
    • 67349191474 scopus 로고    scopus 로고
    • Delay-dependent stability of neutral type neural networks with distributed delays
    • J. Feng, S. Y. Xu, and Y. Zou, Delay-dependent stability of neutral type neural networks with distributed delays, Neurocomputing 72 (2009), 2576-2580.
    • (2009) Neurocomputing , vol.72 , pp. 2576-2580
    • Feng, J.1    Xu, S.Y.2    Zou, Y.3
  • 13
    • 0242270962 scopus 로고    scopus 로고
    • Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays
    • Y. Li, Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays, Chaos Solitons Fractals 20 (2004), no. 3, 459-466.
    • (2004) Chaos Solitons Fractals , vol.20 , Issue.3 , pp. 459-466
    • Li, Y.1
  • 14
    • 8444242130 scopus 로고    scopus 로고
    • Global stability and existence of periodic solutions of discrete delayed cellular neural networks
    • Y. K. Li, Global stability and existence of periodic solutions of discrete delayed cellular neural networks, Phys. Lett. A 333 (2004), no. 1-2, 51-61.
    • (2004) Phys. Lett. A , vol.333 , Issue.1-2 , pp. 51-61
    • Li, Y.K.1
  • 15
    • 8444240791 scopus 로고    scopus 로고
    • Criteria for exponential stability of Cohen-Grossberg neural networks
    • X. Liao, C. Li, and K. Wong, Criteria for exponential stability of Cohen-Grossberg neural networks, Neural Networks 17 (2004), no. 10, 1401-1414.
    • (2004) Neural Networks , vol.17 , Issue.10 , pp. 1401-1414
    • Liao, X.1    Li, C.2    Wong, K.3
  • 16
    • 2442601691 scopus 로고    scopus 로고
    • Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays
    • J. Liang and J. Cao, Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays, Chaos Solitons Fractals 22 (2004), no. 4, 773-785.
    • (2004) Chaos Solitons Fractals , vol.22 , Issue.4 , pp. 773-785
    • Liang, J.1    Cao, J.2
  • 17
    • 12544259222 scopus 로고    scopus 로고
    • Discrete-time bidirectional associative memory neural networks with variable delays
    • L. Liang, J. Cao, and D. Ho, Discrete-time bidirectional associative memory neural networks with variable delays, Phys. Lett. A 335 (2005), 226-234.
    • (2005) Phys. Lett. A , vol.335 , pp. 226-234
    • Liang, L.1    Cao, J.2    Ho, D.3
  • 18
    • 67349190549 scopus 로고    scopus 로고
    • New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type
    • J. A. Liu and G. D. Zong, New delay-dependent asymptotic stability conditions concerning BAM neural networks of neutral type, Neurocomputing 72 (2009), 2549-2555.
    • (2009) Neurocomputing , vol.72 , pp. 2549-2555
    • Liu, J.A.1    Zong, G.D.2
  • 19
    • 34547752308 scopus 로고    scopus 로고
    • + global stability of a Cohen-Grossberg network system with nonnegative equilibria
    • + global stability of a Cohen-Grossberg network system with nonnegative equilibria, Neural Networks 20 (2007), no. 6, 714-722.
    • (2007) Neural Networks , vol.20 , Issue.6 , pp. 714-722
    • Lu, W.L.1    Chen, T.P.2
  • 20
    • 33751247353 scopus 로고    scopus 로고
    • Global attraction and stability for Cohen-Grossberg neural networks with delays
    • K. N. Lu, D. Y. Xu, and Z. C. Yang, Global attraction and stability for Cohen-Grossberg neural networks with delays, Neural Networks 19 (2006), no. 10 1538-1549.
    • (2006) Neural Networks , vol.19 , Issue.10 , pp. 1538-1549
    • Lu, K.N.1    Xu, D.Y.2    Yang, Z.C.3
  • 21
    • 0013046313 scopus 로고    scopus 로고
    • Dynamics of a class of discrete time neural networks and their continuous time counterparts
    • S. Mohamad and K. Gopalsamy, Dynamics of a class of discrete time neural networks and their continuous time counterparts, Math. Comput. Simulation 53 (2000), no. 1-2, 1-39.
    • (2000) Math. Comput. Simulation , vol.53 , Issue.1-2 , pp. 1-39
    • Mohamad, S.1    Gopalsamy, K.2
  • 22
    • 0037440578 scopus 로고    scopus 로고
    • Exponential stability of continuous-time and discrete-time cellular neural networks with delays
    • S. Mohamad and K. Gopalsamy, Exponential stability of continuous-time and discrete-time cellular neural networks with delays, Appl. Math. Comput. 135 (2003), no. 1, 17-38.
    • (2003) Appl. Math. Comput. , vol.135 , Issue.1 , pp. 17-38
    • Mohamad, S.1    Gopalsamy, K.2
  • 23
    • 0036147916 scopus 로고    scopus 로고
    • Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks
    • S. Mohamad and A. G. Naim, Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks, J. Comput. Appl. Math. 138 (2002), no. 1, 1-20.
    • (2002) J. Comput. Appl. Math. , vol.138 , Issue.1 , pp. 1-20
    • Mohamad, S.1    Naim, A.G.2
  • 24
    • 29644435615 scopus 로고    scopus 로고
    • Robust stability of bidirectional associative memory neural networks with time delays
    • Ju H. Park, Robust stability of bidirectional associative memory neural networks with time delays, Phys. Lett. A 349 (2006), no. 6, 494-499.
    • (2006) Phys. Lett. A , vol.349 , Issue.6 , pp. 494-499
    • Park, J.H.1
  • 25
    • 65249134029 scopus 로고    scopus 로고
    • Delay-dependent stability criterion for bidirectional associative memory neural networks with interval time-varying delays
    • Ju H. Park and O. M. Kwon, Delay-dependent stability criterion for bidirectional associative memory neural networks with interval time-varying delays, Modern Physics Letters B 23 (2009), no. 1, 35-46.
    • (2009) Modern Physics Letters B , vol.23 , Issue.1 , pp. 35-46
    • Park, J.H.1    Kwon, O.M.2
  • 26
    • 62949167983 scopus 로고    scopus 로고
    • On exponential stability of associative memory neural networks with time-varying delays
    • Ju H. Park, S. M. Lee, and O. M. Kwon, On exponential stability of associative memory neural networks with time-varying delays, Chaos Solitons Fractals 39 (2009), no. 3, 1083-1091.
    • (2009) Chaos Solitons Fractals , vol.39 , Issue.3 , pp. 1083-1091
    • Park, J.H.1    Lee, S.M.2    Kwon, O.M.3
  • 27
    • 42649106518 scopus 로고    scopus 로고
    • A new stability criterion for bidirectional associative memory neural networks of neutral type
    • Ju 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, Appl. Math. Comput. 199 (2008), no. 2, 716-722.
    • (2008) Appl. Math. Comput. , vol.199 , Issue.2 , pp. 716-722
    • Park, J.H.1    Park, C.H.2    Kwon, O.M.3    Lee, S.M.4
  • 28
    • 33750541311 scopus 로고    scopus 로고
    • New results on the robust stability of Cohen-Grossberg neural networks with delays
    • L. B. Rong and T. P. Chen, New results on the robust stability of Cohen-Grossberg neural networks with delays, Neural Process Lett. 24 (2006), no. 3, 193-202.
    • (2006) Neural Process Lett. , vol.24 , Issue.3 , pp. 193-202
    • Rong, L.B.1    Chen, T.P.2
  • 29
    • 39749090526 scopus 로고    scopus 로고
    • Robust stability in Cohen-Grossberg neural networks with both time-varying and distributed delays
    • Q. K. Song and J. D. Cao, Robust stability in Cohen-Grossberg neural networks with both time-varying and distributed delays, Neural Process Lett. 27 (2008), no. 2, 179-196.
    • (2008) Neural Process Lett. , vol.27 , Issue.2 , pp. 179-196
    • Song, Q.K.1    Cao, J.D.2
  • 30
    • 11144309685 scopus 로고    scopus 로고
    • Discrete-time analogues of intergrodifferential equations modelling neural networks
    • C. Sun and C. B. Feng, Discrete-time analogues of intergrodifferential equations modelling neural networks, Phys. Lett. A 334 (2005), 180-191.
    • (2005) Phys. Lett. A , vol.334 , pp. 180-191
    • Sun, C.1    Feng, C.B.2
  • 31
    • 22544452748 scopus 로고    scopus 로고
    • Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays
    • J. Sun and L. Wang, Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays, Phys. D 208 (2005), no. 1-2, 1-20.
    • (2005) Phys. D , vol.208 , Issue.1-2 , pp. 1-20
    • Sun, J.1    Wang, L.2
  • 32
    • 8344232332 scopus 로고    scopus 로고
    • Stability of Cohen-Grossberg neural networks with distributed delays
    • L. Wang, Stability of Cohen-Grossberg neural networks with distributed delays, Appl. Math. Comput. 160 (2005), no. 1, 93-110.
    • (2005) Appl. Math. Comput. , vol.160 , Issue.1 , pp. 93-110
    • Wang, L.1
  • 33
    • 33646512597 scopus 로고    scopus 로고
    • Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
    • Z. D. Wang, Y. R. Liu, and M. Li, Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans. Neural Networks 17 (2006), no. 3, 814-820.
    • (2006) IEEE Trans. Neural Networks , vol.17 , Issue.3 , pp. 814-820
    • Wang, Z.D.1    Liu, Y.R.2    Li, M.3
  • 34
    • 24344504017 scopus 로고    scopus 로고
    • On global asymptotic stability of neural networks with discrete and distributed delays
    • Z. D. Wang, Y. R. Liu, and X. H. Liu, On global asymptotic stability of neural networks with discrete and distributed delays, Phys Lett. A 345 (2005), no. 4-6, 299-308.
    • (2005) Phys Lett. A , vol.345 , Issue.4-6 , pp. 299-308
    • Wang, Z.D.1    Liu, Y.R.2    Liu, X.H.3
  • 35
    • 33846014280 scopus 로고    scopus 로고
    • Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time varying delays
    • W. Wu, B. T. Cui, and X. Y. Lou, Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time varying delays, Neurocomputing 70 (2007), no. 4-6, 1085-1088.
    • (2007) Neurocomputing , vol.70 , Issue.4-6 , pp. 1085-1088
    • Wu, W.1    Cui, B.T.2    Lou, X.Y.3
  • 36
    • 15844417389 scopus 로고    scopus 로고
    • Global exponential stability of discrete-time Cohen-Grossberg neural networks
    • W. Xiong and J. Cao, Global exponential stability of discrete-time Cohen-Grossberg neural networks, Neurocomputing 64 (2005), 433-446.
    • (2005) Neurocomputing , vol.64 , pp. 433-446
    • Xiong, W.1    Cao, J.2
  • 37
    • 61849131250 scopus 로고    scopus 로고
    • Exponential stability of periodic solution to Cohen-Grossberg type BAM neural networks with time-varying delays
    • H. J. Xiang and J. D. Cao, Exponential stability of periodic solution to Cohen-Grossberg type BAM neural networks with time-varying delays, Neurocomputing 72 (2009), no. 7-8, 1702-1711.
    • (2009) Neurocomputing , vol.72 , Issue.7-8 , pp. 1702-1711
    • Xiang, H.J.1    Cao, J.D.2
  • 38
    • 34548385611 scopus 로고    scopus 로고
    • An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural networks via nonsmooth analysis
    • W. W. Yu, J. D. Cao, and J. Wang, An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural networks via nonsmooth analysis, Neural Networks 20 (2007), no. 7, 810-818.
    • (2007) Neural Networks , vol.20 , Issue.7 , pp. 810-818
    • Yu, W.W.1    Cao, J.D.2    Wang, J.3
  • 39
    • 33751212466 scopus 로고    scopus 로고
    • Global exponential stability of recurrent networks with time-varying delays in the presence of strong external stimuli
    • Z. G. Zeng, J.W, Global exponential stability of recurrent networks with time-varying delays in the presence of strong external stimuli, Neural Networks 19 (2006), no. 10, 1528-1537.
    • (2006) Neural Networks , vol.19 , Issue.10 , pp. 1528-1537
    • Zeng, Z.G.J.W.1
  • 40
    • 15744372086 scopus 로고    scopus 로고
    • Global exponential stability of Cohen-Grossberg neural networks with variable delays
    • J. Zhang, Y. Suda, and H. Komine, Global exponential stability of Cohen-Grossberg neural networks with variable delays, Phys. Lett. A 338 (2005), no. 1, 44-50.
    • (2005) Phys. Lett. A , vol.338 , Issue.1 , pp. 44-50
    • Zhang, J.1    Suda, Y.2    Komine, H.3
  • 41
    • 77955198711 scopus 로고    scopus 로고
    • Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks
    • Z. Q. Zhang and 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), no. 5, 763-780.
    • (2010) J. Franklin Inst. , vol.347 , Issue.5 , pp. 763-780
    • Zhang, Z.Q.1    Zhou, D.M.2
  • 42
    • 33750062596 scopus 로고    scopus 로고
    • Hopf bifucation in Cohen-Grossberg neural network with discrete delays
    • H. Y. Zhao and L. Wang, Hopf bifucation in Cohen-Grossberg neural network with discrete delays, Nonlinear Anal.: Real World Appli. 8 (2007), no. 1, 73-89.
    • (2007) Nonlinear Anal.: Real World Appli. , vol.8 , Issue.1 , pp. 73-89
    • Zhao, H.Y.1    Wang, L.2
  • 43
    • 34548163664 scopus 로고    scopus 로고
    • Periodic oscillation of discrete-time bidirectional associative memory neural networks
    • H. Zhao, L. Sun, and G. Wang, Periodic oscillation of discrete-time bidirectional associative memory neural networks, Neurocomputing 70 (2007), 2924-2930.
    • (2007) Neurocomputing , vol.70 , pp. 2924-2930
    • Zhao, H.1    Sun, L.2    Wang, G.3
  • 44
    • 33751510165 scopus 로고    scopus 로고
    • Existence and global exponential stability of periodic solution for discrete time BAM neural networks
    • T. Zhou, Y. Liu, and Y. C. Liu, Existence and global exponential stability of periodic solution for discrete time BAM neural networks, Appl. Math. Comput. 182 (2006), no. 2, 1341-1354.
    • (2006) Appl. Math. Comput. , vol.182 , Issue.2 , pp. 1341-1354
    • Zhou, T.1    Liu, Y.2    Liu, Y.C.3
  • 45
    • 56549104601 scopus 로고    scopus 로고
    • New results for global stability of Cohen-Grossberg neural networks with multiple time delays
    • Z. Orman and S. Arik, New results for global stability of Cohen-Grossberg neural networks with multiple time delays, Neurocomputing 71 (2008), no. 16-18, 3053-3063.
    • (2008) Neurocomputing , vol.71 , Issue.16-18 , pp. 3053-3063
    • Orman, Z.1    Arik, S.2


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