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Volumn 35, Issue 1, 2008, Pages 116-125

Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; DIFFUSION; LYAPUNOV FUNCTIONS; NUMERICAL METHODS; SYSTEMS ANALYSIS;

EID: 34548525395     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.05.002     Document Type: Article
Times cited : (281)

References (48)
  • 1
    • 0027659604 scopus 로고
    • Analysis and design of a recurrent neural network for linear programming
    • Wang J. Analysis and design of a recurrent neural network for linear programming. IEEE Trans Circ Syst I 40 (1993) 613-618
    • (1993) IEEE Trans Circ Syst I , vol.40 , pp. 613-618
    • Wang, J.1
  • 2
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcuss C.M., and Westervelt R.M. Stability of analog neural networks with delay. Phys Rev A 39 1 (1989) 347-359
    • (1989) Phys Rev A , vol.39 , Issue.1 , pp. 347-359
    • Marcuss, C.M.1    Westervelt, R.M.2
  • 4
    • 0028468031 scopus 로고
    • How delays affect neural dynamics and learning
    • Baldi P., and Atiga A.F. How delays affect neural dynamics and learning. IEEE Trans Neural Networks 5 (1994) 612-621
    • (1994) IEEE Trans Neural Networks , vol.5 , pp. 612-621
    • Baldi, P.1    Atiga, A.F.2
  • 5
    • 0026882236 scopus 로고
    • Stability and dynamics of delay-type general and cellular neural networks
    • Roska T., Wu C.W., Balsi M., and Chua L.O. Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans Circ Syst I 39 (1992) 487-490
    • (1992) IEEE Trans Circ Syst I , vol.39 , pp. 487-490
    • Roska, T.1    Wu, C.W.2    Balsi, M.3    Chua, L.O.4
  • 6
    • 0027582973 scopus 로고
    • Stability of cellular neural networks with dominant nonlinear and delay-type templates
    • Roska T., Wu C.W., and Chua L.O. Stability of cellular neural networks with dominant nonlinear and delay-type templates. IEEE Trans Circ Syst I 40 (1993) 270-272
    • (1993) IEEE Trans Circ Syst I , vol.40 , pp. 270-272
    • Roska, T.1    Wu, C.W.2    Chua, L.O.3
  • 7
    • 0028484639 scopus 로고
    • Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions
    • Gilli M. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Trans Circ Syst I 41 (1994) 518-528
    • (1994) IEEE Trans Circ Syst I , vol.41 , pp. 518-528
    • Gilli, M.1
  • 8
    • 0001075269 scopus 로고
    • Stability in asymmetric Hopfield nets with transmission delays
    • Gopalsamy K., and He X.Z. Stability in asymmetric Hopfield nets with transmission delays. Phys D 76 (1994) 344-358
    • (1994) Phys D , vol.76 , pp. 344-358
    • Gopalsamy, K.1    He, X.Z.2
  • 9
    • 0028542772 scopus 로고
    • Delay-independent stability in bidirectional associative memory networks
    • Gopalsamy K., and He X.Z. Delay-independent stability in bidirectional associative memory networks. IEEE Trans Neural Networks 5 (1994) 998-1002
    • (1994) IEEE Trans Neural Networks , vol.5 , pp. 998-1002
    • Gopalsamy, K.1    He, X.Z.2
  • 10
    • 0000791959 scopus 로고
    • Global stability and local stability of Hopfield neural networks with delays
    • Ye H., Michel A.N., and Wang K. Global stability and local stability of Hopfield neural networks with delays. Phys Rev E 50 (1994) 4206-4213
    • (1994) Phys Rev E , vol.50 , pp. 4206-4213
    • Ye, H.1    Michel, A.N.2    Wang, K.3
  • 11
    • 0029345226 scopus 로고
    • New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Forti M., and Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circ Syst I 42 (1995) 354-366
    • (1995) IEEE Trans Circ Syst I , vol.42 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 12
    • 0002328180 scopus 로고    scopus 로고
    • On the global convergence of a class of functional differential equations with applications in neural network theory
    • Joy M.P. On the global convergence of a class of functional differential equations with applications in neural network theory. J Math Anal Appl 232 (1999) 61-81
    • (1999) J Math Anal Appl , vol.232 , pp. 61-81
    • Joy, M.P.1
  • 13
    • 0034233270 scopus 로고    scopus 로고
    • Results concerning the absolute stability of delayed neural networks
    • Joy M.P. Results concerning the absolute stability of delayed neural networks. Neural Networks 13 (2000) 613-616
    • (2000) Neural Networks , vol.13 , pp. 613-616
    • Joy, M.P.1
  • 14
    • 0036737354 scopus 로고    scopus 로고
    • An analysis of global asymptotic stability of delayed cellular networks
    • Arik S. An analysis of global asymptotic stability of delayed cellular networks. IEEE Trans Neural Networks 13 (2002) 1239-1242
    • (2002) IEEE Trans Neural Networks , vol.13 , pp. 1239-1242
    • Arik, S.1
  • 15
    • 0242608076 scopus 로고    scopus 로고
    • Global asymptotic stability of a large class of neural networks with constant time delay
    • Arik S. Global asymptotic stability of a large class of neural networks with constant time delay. Phys Lett A 311 (2003) 504-511
    • (2003) Phys Lett A , vol.311 , pp. 504-511
    • Arik, S.1
  • 16
    • 0035365656 scopus 로고    scopus 로고
    • Convergence analysis of cellular neural networks with unbounded delay
    • Zhang Y., Heng P.A., and Leung K.S. Convergence analysis of cellular neural networks with unbounded delay. IEEE Trans Circ Syst I 48 6 (2001) 680-687
    • (2001) IEEE Trans Circ Syst I , vol.48 , Issue.6 , pp. 680-687
    • Zhang, Y.1    Heng, P.A.2    Leung, K.S.3
  • 17
    • 28444431612 scopus 로고    scopus 로고
    • Global convergence of Lotka-Volterra recurrent neural networks with delays
    • Zhang Y., and Kok Kiong T. Global convergence of Lotka-Volterra recurrent neural networks with delays. IEEE Trans Circ Syst I 52 11 (2005) 2482-2489
    • (2005) IEEE Trans Circ Syst I , vol.52 , Issue.11 , pp. 2482-2489
    • Zhang, Y.1    Kok Kiong, T.2
  • 18
    • 24044465139 scopus 로고    scopus 로고
    • Global asymptotic stability and global exponential stability of delayed cellular neural networks
    • Liao X.X., Wang J., and Zeng Z. Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Trans Circ Syst II 52 7 (2005) 403-409
    • (2005) IEEE Trans Circ Syst II , vol.52 , Issue.7 , pp. 403-409
    • Liao, X.X.1    Wang, J.2    Zeng, Z.3
  • 19
    • 33646523344 scopus 로고    scopus 로고
    • Improved conditions for global exponential stability of recurrent neural networks with time-varying delays
    • Zeng Z., and Wang J. Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans Neural Networks 17 3 (2006) 623-635
    • (2006) IEEE Trans Neural Networks , vol.17 , Issue.3 , pp. 623-635
    • Zeng, Z.1    Wang, J.2
  • 20
    • 4644236344 scopus 로고    scopus 로고
    • Global robust stability of interval cellular neural networks with time-varying delays
    • Chen A.P., Cao J.D., and Huang L.H. Global robust stability of interval cellular neural networks with time-varying delays. Chaos, Solitons & Fractals 23 3 (2005) 787-799
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.3 , pp. 787-799
    • Chen, A.P.1    Cao, J.D.2    Huang, L.H.3
  • 21
    • 17544394696 scopus 로고    scopus 로고
    • Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays
    • Liao X.F., Wong K.W., and Yang S.Z. Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays. Phys Lett A 316 1-2 (2003) 55-64
    • (2003) Phys Lett A , vol.316 , Issue.1-2 , pp. 55-64
    • Liao, X.F.1    Wong, K.W.2    Yang, S.Z.3
  • 22
    • 0344876153 scopus 로고    scopus 로고
    • Global exponential convergence analysis of delayed neural networks with time-varying delays
    • Zhang Q., Wei X.P., and Xu J. Global exponential convergence analysis of delayed neural networks with time-varying delays. Phys Lett A 318 (2003) 537-544
    • (2003) Phys Lett A , vol.318 , pp. 537-544
    • Zhang, Q.1    Wei, X.P.2    Xu, J.3
  • 23
    • 0036647562 scopus 로고    scopus 로고
    • LMI-based approach for asymptotical stability analysis of delayed neural networks
    • Liao X.F., Chen G., and Sanchez E.N. LMI-based approach for asymptotical stability analysis of delayed neural networks. IEEE Trans Circ Syst I 49 (2002) 1033-1039
    • (2002) IEEE Trans Circ Syst I , vol.49 , pp. 1033-1039
    • Liao, X.F.1    Chen, G.2    Sanchez, E.N.3
  • 24
    • 1942519336 scopus 로고    scopus 로고
    • Some sufficient conditions for global exponential stability of delayed Hopfield neural networks
    • Lu H.T., Chung F.L., and He Z.Y. Some sufficient conditions for global exponential stability of delayed Hopfield neural networks. Neural Networks 17 (2004) 537-544
    • (2004) Neural Networks , vol.17 , pp. 537-544
    • Lu, H.T.1    Chung, F.L.2    He, Z.Y.3
  • 25
    • 0034849714 scopus 로고    scopus 로고
    • Global exponential stability of delayed hopfield neural networks
    • Chen T.P. Global exponential stability of delayed hopfield neural networks. Neural Networks 14 (2001) 977-980
    • (2001) Neural Networks , vol.14 , pp. 977-980
    • Chen, T.P.1
  • 26
    • 0142087577 scopus 로고    scopus 로고
    • Delay-independent stability analysis of Cohen-Grossberg neural networks
    • Chen T.P., and Rong L.B. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys Lett A 317 (2003) 436-449
    • (2003) Phys Lett A , vol.317 , pp. 436-449
    • Chen, T.P.1    Rong, L.B.2
  • 27
    • 0037303380 scopus 로고    scopus 로고
    • Global exponential stability of neural networks with variable delays
    • Zhang J.Y. Global exponential stability of neural networks with variable delays. IEEE Trans Circ Syst I 50 (2003) 288-291
    • (2003) IEEE Trans Circ Syst I , vol.50 , pp. 288-291
    • Zhang, J.Y.1
  • 28
    • 1642373914 scopus 로고    scopus 로고
    • Absolutely exponential stability of a class of neural networks with unbounded delay
    • Zhang J.Y., Suda Y., and Iwasa T. Absolutely exponential stability of a class of neural networks with unbounded delay. Neural Networks 17 (2004) 391-397
    • (2004) Neural Networks , vol.17 , pp. 391-397
    • Zhang, J.Y.1    Suda, Y.2    Iwasa, T.3
  • 29
    • 0036125925 scopus 로고    scopus 로고
    • A new approach to stability of neural networks with time-varying delays
    • Peng J., Qiao H., and Xu Z. A new approach to stability of neural networks with time-varying delays. Neural Networks 15 (2002) 95-103
    • (2002) Neural Networks , vol.15 , pp. 95-103
    • Peng, J.1    Qiao, H.2    Xu, Z.3
  • 30
    • 13444256385 scopus 로고    scopus 로고
    • A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach
    • Cao J.D., and Ho D.W.C. A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos, Solitons & Fractals 24 (2005) 1317-1329
    • (2005) Chaos, Solitons & Fractals , vol.24 , pp. 1317-1329
    • Cao, J.D.1    Ho, D.W.C.2
  • 31
    • 20144369395 scopus 로고    scopus 로고
    • Global exponential stability and periodicity of recurrent neural networks with time delays
    • Cao J.D., and Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuits Syst I 52 5 (2005) 925-931
    • (2005) IEEE Trans Circuits Syst I , vol.52 , Issue.5 , pp. 925-931
    • Cao, J.D.1    Wang, J.2
  • 32
    • 4243149477 scopus 로고    scopus 로고
    • Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction diffusion terms
    • Song Q.K., and Cao J.D. Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction diffusion terms. Chaos, Solitons & Fractals 23 2 (2005) 421-430
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.2 , pp. 421-430
    • Song, Q.K.1    Cao, J.D.2
  • 33
    • 24944581606 scopus 로고    scopus 로고
    • Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays
    • Song Q.K., Cao J.D., and Zhao Z.J. Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Anal: Real World Appl 7 1 (2006) 65-80
    • (2006) Nonlinear Anal: Real World Appl , vol.7 , Issue.1 , pp. 65-80
    • Song, Q.K.1    Cao, J.D.2    Zhao, Z.J.3
  • 34
    • 22844446369 scopus 로고    scopus 로고
    • Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays
    • Zhao H.Y., and Wang G.L. Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays. Phys Lett A 343 5 (2005) 372-383
    • (2005) Phys Lett A , vol.343 , Issue.5 , pp. 372-383
    • Zhao, H.Y.1    Wang, G.L.2
  • 35
    • 0041661956 scopus 로고    scopus 로고
    • Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays
    • Liang J.L., and Cao J.D. Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays. Phys Lett A 314 (2003) 434-442
    • (2003) Phys Lett A , vol.314 , pp. 434-442
    • Liang, J.L.1    Cao, J.D.2
  • 36
    • 12544251852 scopus 로고    scopus 로고
    • Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms
    • Song Q.K., Zhao Z.J., and Li Y.M. Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms. Phys Lett A 335 2-3 (2005) 213-225
    • (2005) Phys Lett A , vol.335 , Issue.2-3 , pp. 213-225
    • Song, Q.K.1    Zhao, Z.J.2    Li, Y.M.3
  • 37
    • 24944480285 scopus 로고    scopus 로고
    • Global asymptotic stability of BAM neural networks with distributed delays and reaction-diffusion terms
    • Cui B.T., and Lou X.Y. Global asymptotic stability of BAM neural networks with distributed delays and reaction-diffusion terms. Chaos, Solitons & Fractals 27 5 (2006) 1347-1354
    • (2006) Chaos, Solitons & Fractals , vol.27 , Issue.5 , pp. 1347-1354
    • Cui, B.T.1    Lou, X.Y.2
  • 38
    • 31144468063 scopus 로고    scopus 로고
    • Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays
    • Wang L.S., and Gao Y.Y. Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays. Phys Lett A 350 5-6 (2006) 342-348
    • (2006) Phys Lett A , vol.350 , Issue.5-6 , pp. 342-348
    • Wang, L.S.1    Gao, Y.Y.2
  • 39
    • 33646563410 scopus 로고    scopus 로고
    • Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays
    • Zhao Z.J., Song Q.K., and Zhang J.Y. Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays. Comput Math Appl 51 3-4 (2006) 475-486
    • (2006) Comput Math Appl , vol.51 , Issue.3-4 , pp. 475-486
    • Zhao, Z.J.1    Song, Q.K.2    Zhang, J.Y.3
  • 40
    • 24144481927 scopus 로고    scopus 로고
    • Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with delays
    • Sun J., and Wan L. Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with delays. Int J Bifurc Chaos 15 7 (2005) 2131-2144
    • (2005) Int J Bifurc Chaos , vol.15 , Issue.7 , pp. 2131-2144
    • Sun, J.1    Wan, L.2
  • 41
    • 0038349337 scopus 로고    scopus 로고
    • Asymptotic behavior of a class of reaction-diffusion equations with delays
    • Wang L.S., and Xu D.Y. Asymptotic behavior of a class of reaction-diffusion equations with delays. J Math Anal Appl 281 (2003) 439-453
    • (2003) J Math Anal Appl , vol.281 , pp. 439-453
    • Wang, L.S.1    Xu, D.Y.2
  • 43
    • 0035372163 scopus 로고    scopus 로고
    • Hopf bifurcation and chaos in a single delayed neuron equation with non monotonic activation function
    • Liao X.F., Wong K.W., Leung C.S., and Wu Z.F. Hopf bifurcation and chaos in a single delayed neuron equation with non monotonic activation function. Chaos, Solitons & Fractals 12 (2001) 1535-1547
    • (2001) Chaos, Solitons & Fractals , vol.12 , pp. 1535-1547
    • Liao, X.F.1    Wong, K.W.2    Leung, C.S.3    Wu, Z.F.4
  • 44
    • 0031140839 scopus 로고    scopus 로고
    • Stability in Gilpin-Ayala competition models with diffusion
    • Liao X.X., and Li J. Stability in Gilpin-Ayala competition models with diffusion. Nonlinear Anal 28 (1997) 1751-1758
    • (1997) Nonlinear Anal , vol.28 , pp. 1751-1758
    • Liao, X.X.1    Li, J.2
  • 45
    • 0018174331 scopus 로고
    • Global stability in Lotka-Volterra systems with diffusion
    • Hastings A. Global stability in Lotka-Volterra systems with diffusion. J Math Biol 6 2 (1978) 163-168
    • (1978) J Math Biol , vol.6 , Issue.2 , pp. 163-168
    • Hastings, A.1
  • 46
    • 0017151487 scopus 로고
    • Convergence to the equilibrium state in the Volterra-Lotka diffusion equations
    • Rothe F. Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J Math Biol 3 (1976) 319-324
    • (1976) J Math Biol , vol.3 , pp. 319-324
    • Rothe, F.1


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