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Volumn 23, Issue 7, 2010, Pages 805-811

Stability analysis of recurrent neural networks with piecewise constant argument of generalized type

Author keywords

Method of Lyapunov functions; Neural networks; Piecewise constant argument of generalized type

Indexed keywords

DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; NEURAL NETWORKS;

EID: 77955056707     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2010.05.006     Document Type: Article
Times cited : (67)

References (58)
  • 1
    • 70349849327 scopus 로고    scopus 로고
    • On the integral manifolds of the differential equations with piecewise constant argument of generalized type
    • Hindawi Publishing Corporation, R.P. Agarval, K. Perera (Eds.)
    • Akhmet M.U. On the integral manifolds of the differential equations with piecewise constant argument of generalized type. Proceedings of the conference on differential and difference equations at the Florida Institute of Technology 2006, 11-20. Hindawi Publishing Corporation. R.P. Agarval, K. Perera (Eds.).
    • (2006) Proceedings of the conference on differential and difference equations at the Florida Institute of Technology , pp. 11-20
    • Akhmet, M.U.1
  • 2
    • 34547127132 scopus 로고    scopus 로고
    • On the reduction principle for differential equations with piecewise constant argument of generalized type
    • Akhmet M.U. On the reduction principle for differential equations with piecewise constant argument of generalized type. Journal of Mathematical Analysis and Applications 2007, 336:646-663.
    • (2007) Journal of Mathematical Analysis and Applications , vol.336 , pp. 646-663
    • Akhmet, M.U.1
  • 3
    • 36749034215 scopus 로고    scopus 로고
    • Stability of differential equations with piecewise constant arguments of generalized type
    • Akhmet M.U. Stability of differential equations with piecewise constant arguments of generalized type. Nonlinear Analysis 2008, 68:794-803.
    • (2008) Nonlinear Analysis , vol.68 , pp. 794-803
    • Akhmet, M.U.1
  • 4
    • 40949101730 scopus 로고    scopus 로고
    • Almost periodic solutions of differential equations with piecewise constant argument of generalized type
    • Akhmet M.U. Almost periodic solutions of differential equations with piecewise constant argument of generalized type. Nonlinear Analysis: Hybrid Systems 2008, 2:456-467.
    • (2008) Nonlinear Analysis: Hybrid Systems , vol.2 , pp. 456-467
    • Akhmet, M.U.1
  • 6
    • 70349854717 scopus 로고    scopus 로고
    • Lyapunov-Razumikhin method for differential equations with piecewise constant argument
    • Akhmet M.U., Aruǧaslan D. Lyapunov-Razumikhin method for differential equations with piecewise constant argument. Discrete and Continuous Dynamical Systems 2009, 25(2):457-466.
    • (2009) Discrete and Continuous Dynamical Systems , vol.25 , Issue.2 , pp. 457-466
    • Akhmet, M.U.1    Aruǧaslan, D.2
  • 8
    • 77955049962 scopus 로고    scopus 로고
    • Method of Lyapunov functions for differential equations with piecewise constant delay. Journal of Computational and Applied Mathematics (in press)
    • Akhmet, M. U., Aruǧaslan, D., & Yilmaz, E. Method of Lyapunov functions for differential equations with piecewise constant delay. Journal of Computational and Applied Mathematics (in press).
    • Akhmet, M.U.1    Aruǧaslan, D.2    Yilmaz, E.3
  • 9
    • 77949489150 scopus 로고    scopus 로고
    • Differential equations with state-dependent piecewise constant argument
    • Akhmet M.U., Büyükadali C. Differential equations with state-dependent piecewise constant argument. Nonlinear Analysis 2010, 72:4200-4210.
    • (2010) Nonlinear Analysis , vol.72 , pp. 4200-4210
    • Akhmet, M.U.1    Büyükadali, C.2
  • 10
    • 77955055626 scopus 로고    scopus 로고
    • Impulsive Hopfield-type neural network system with piecewise constant argument. Nonlinear Analysis: Real World Applications(in press).
    • Akhmet, M. U., & Yilmaz, E. Impulsive Hopfield-type neural network system with piecewise constant argument. Nonlinear Analysis: Real World Applications(in press).
    • Akhmet, M.U.1    Yilmaz, E.2
  • 11
    • 0036737354 scopus 로고    scopus 로고
    • An analysis of global asymptotic stability of delayed cellular neural networks
    • Arik S. An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks 2002, 13:1239-1242.
    • (2002) IEEE Transactions on Neural Networks , vol.13 , pp. 1239-1242
    • Arik, S.1
  • 13
    • 0014426440 scopus 로고
    • Mechanism of rhythmic synchronous flashing of fireflies: fireflies of Southeast Asia may use anticipatory time-measuring in synchronizing their flashing
    • Buck J., Buck E. Mechanism of rhythmic synchronous flashing of fireflies: fireflies of Southeast Asia may use anticipatory time-measuring in synchronizing their flashing. Science 1968, 159:1319-1327.
    • (1968) Science , vol.159 , pp. 1319-1327
    • Buck, J.1    Buck, E.2
  • 14
    • 0035507277 scopus 로고    scopus 로고
    • Global stability conditions for delayed CNNs
    • Cao J. Global stability conditions for delayed CNNs. IEEE Transactions on Circuits and Systems I 2001, 48:1330-1333.
    • (2001) IEEE Transactions on Circuits and Systems I , vol.48 , pp. 1330-1333
    • Cao, J.1
  • 15
    • 0345984486 scopus 로고    scopus 로고
    • On stability of delayed cellular neural networks
    • Cao J. On stability of delayed cellular neural networks. Physics Letters A 1999, 261:303-308.
    • (1999) Physics Letters A , vol.261 , pp. 303-308
    • Cao, J.1
  • 16
    • 0034309351 scopus 로고    scopus 로고
    • Global asymptotic stability of neural networks with transmission delays
    • Cao J. Global asymptotic stability of neural networks with transmission delays. International Journal of Systems Science 2000, 31:1313-1316.
    • (2000) International Journal of Systems Science , vol.31 , pp. 1313-1316
    • Cao, J.1
  • 17
    • 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 2001, 14:977-980.
    • (2001) Neural Networks , vol.14 , pp. 977-980
    • Chen, T.P.1
  • 18
    • 0035292684 scopus 로고    scopus 로고
    • Exponential convergence of delayed dynamical systems
    • Chen T.P., Amari S. Exponential convergence of delayed dynamical systems. Neural Computation 2001, 13(3):621-636.
    • (2001) Neural Computation , vol.13 , Issue.3 , pp. 621-636
    • Chen, T.P.1    Amari, S.2
  • 20
    • 0025632457 scopus 로고
    • Stability of a class of nonreciprocal cellular neural networks
    • Chua L.O., Roska T. Stability of a class of nonreciprocal cellular neural networks. IEEE Transactions on Circuits and Systems 1990, 37:1520-1527.
    • (1990) IEEE Transactions on Circuits and Systems , vol.37 , pp. 1520-1527
    • Chua, L.O.1    Roska, T.2
  • 21
    • 0026913847 scopus 로고
    • Cellular neural networks with nonlinear and delay type template elements and non-uniform grids
    • Chua L.O., Roska T. Cellular neural networks with nonlinear and delay type template elements and non-uniform grids. International Journal of Circuit Theory and Applications 1992, 20:449-451.
    • (1992) International Journal of Circuit Theory and Applications , vol.20 , pp. 449-451
    • Chua, L.O.1    Roska, T.2
  • 22
    • 77955057968 scopus 로고
    • Cellular neural networks with nonlinear and delay-type template elements. In Proc. 1990 IEEE int. workshop on cellular neural networks and their applications
    • Chua, L.O., & Roska, T. (1990). Cellular neural networks with nonlinear and delay-type template elements. In Proc. 1990 IEEE int. workshop on cellular neural networks and their applications (pp. 12-25).
    • (1990) , pp. 12-25
    • Chua, L.O.1    Roska, T.2
  • 27
    • 0032298907 scopus 로고    scopus 로고
    • Global attractivity in delayed Hopfield neural network models
    • Driessche P.V.D., Zou X. Global attractivity in delayed Hopfield neural network models. SIAM Journal on Applied Mathematics 1998, 58(6):1878-1890.
    • (1998) SIAM Journal on Applied Mathematics , vol.58 , Issue.6 , pp. 1878-1890
    • Driessche, P.V.D.1    Zou, X.2
  • 28
    • 0038332350 scopus 로고
    • Can the future influence the present?
    • Driver R.D. Can the future influence the present?. Physical Review D 1979, 19:1098-1107.
    • (1979) Physical Review D , vol.19 , pp. 1098-1107
    • Driver, R.D.1
  • 29
    • 0029345226 scopus 로고
    • New conditions for global stability of neural networks with application to linear and quadratic programming problems
    • Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Transactions on Circuits and Systems I 1995, 42:354-366.
    • (1995) IEEE Transactions on Circuits and Systems I , vol.42 , pp. 354-366
    • Forti, M.1    Tesi, A.2
  • 34
    • 0037124336 scopus 로고    scopus 로고
    • Global exponential stability and periodic solutions of recurrent neural networks with delays
    • Huang H., Cao J., Wang J. Global exponential stability and periodic solutions of recurrent neural networks with delays. Physics Letters A 2002, 298:393-404.
    • (2002) Physics Letters A , vol.298 , pp. 393-404
    • Huang, H.1    Cao, J.2    Wang, J.3
  • 36
    • 0036608391 scopus 로고    scopus 로고
    • Stability analyses of cellular neural networks with continuous time delay
    • Liao X., Wu Z., Yu J. Stability analyses of cellular neural networks with continuous time delay. Journal of Computational and Applied Mathematics 2002, 143:29-47.
    • (2002) Journal of Computational and Applied Mathematics , vol.143 , pp. 29-47
    • Liao, X.1    Wu, Z.2    Yu, J.3
  • 38
    • 0037440578 scopus 로고    scopus 로고
    • Exponential stability of continuous-time and discrete-time cellular neural networks with delays
    • Mohamad S., Gopalsamy K. Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation 2003, 135:17-38.
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 17-38
    • Mohamad, S.1    Gopalsamy, K.2
  • 39
    • 0346582863 scopus 로고    scopus 로고
    • Mathematical biology: I. an introduction
    • Springer-Verlag, New York, Heidelberg, Berlin
    • Murray J.D. Mathematical biology: I. an introduction. Interdisciplinary applied mathematics 2002, Vol. 17. Springer-Verlag, New York, Heidelberg, Berlin. third ed.
    • (2002) Interdisciplinary applied mathematics , vol.Vol. 17
    • Murray, J.D.1
  • 40
    • 33845795754 scopus 로고    scopus 로고
    • Global exponential stability of cellular neural networks with variable delays
    • Park J.H. Global exponential stability of cellular neural networks with variable delays. Applied Mathematics and Computation 2006, 183:1214-1219.
    • (2006) Applied Mathematics and Computation , vol.183 , pp. 1214-1219
    • Park, J.H.1
  • 41
    • 84872778115 scopus 로고
    • Advanced differential equations with piecewise constant argument deviations
    • Shah S.M., Wiener J. Advanced differential equations with piecewise constant argument deviations. International Journal of Mathematical Sciences 1983, 6:671-703.
    • (1983) International Journal of Mathematical Sciences , vol.6 , pp. 671-703
    • Shah, S.M.1    Wiener, J.2
  • 42
    • 56449106923 scopus 로고    scopus 로고
    • Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach
    • Song Q. Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Neurocomputing 2008, 71(13-15):2823-2830.
    • (2008) Neurocomputing , vol.71 , Issue.13-15 , pp. 2823-2830
    • Song, Q.1
  • 43
    • 0037732525 scopus 로고    scopus 로고
    • Deformation of traveling waves in delayed cellular neural networks
    • Weng P., Wu J. Deformation of traveling waves in delayed cellular neural networks. International Journal of Bifurcation and Chaos 2003, 13(4):797-813.
    • (2003) International Journal of Bifurcation and Chaos , vol.13 , Issue.4 , pp. 797-813
    • Weng, P.1    Wu, J.2
  • 45
    • 33644982553 scopus 로고    scopus 로고
    • New results on global exponential stability of recurrent neural networks with time-varying delays
    • Xu S., Chu Y., Lu J. New results on global exponential stability of recurrent neural networks with time-varying delays. Physics Letters A 2006, 352:371-379.
    • (2006) Physics Letters A , vol.352 , pp. 371-379
    • Xu, S.1    Chu, Y.2    Lu, J.3
  • 47
    • 32144445292 scopus 로고    scopus 로고
    • New estimate on the domains of attraction of equilibrium points in continuous Hopfield neural networks
    • Yang X., Liao X., Li C., Evans D.J. New estimate on the domains of attraction of equilibrium points in continuous Hopfield neural networks. Physics Letters A 2006, 351:161-166.
    • (2006) Physics Letters A , vol.351 , pp. 161-166
    • Yang, X.1    Liao, X.2    Li, C.3    Evans, D.J.4
  • 48
    • 33751212466 scopus 로고    scopus 로고
    • Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli
    • Zeng Z., Wang J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Networks 2006, 19:1528-1537.
    • (2006) Neural Networks , vol.19 , pp. 1528-1537
    • Zeng, Z.1    Wang, J.2
  • 49
    • 33646523344 scopus 로고    scopus 로고
    • Improved conditions for global exponential stability of recurrent neural networks with time-varying delays
    • Zeng Z., Wang J. Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks 2006, 17(3):623-635.
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.3 , pp. 623-635
    • Zeng, Z.1    Wang, J.2
  • 50
    • 33646523344 scopus 로고    scopus 로고
    • Improved conditions for global exponential stability of recurrent neural networks with time-varying delays
    • Zeng Z.G., Wang J. Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks 2006, 17(3):623-635.
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.3 , pp. 623-635
    • Zeng, Z.G.1    Wang, J.2
  • 51
    • 0142165161 scopus 로고    scopus 로고
    • Global exponential stability of a general class of recurrent neural networks with time-varying delays
    • Zeng Z., Wang J., Liao X. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I 2003, 50(10):1353-1358.
    • (2003) IEEE Transactions on Circuits and Systems I , vol.50 , Issue.10 , pp. 1353-1358
    • Zeng, Z.1    Wang, J.2    Liao, X.3
  • 52
    • 0037303380 scopus 로고    scopus 로고
    • Globally exponential stability of neural networks with variable delays
    • Zhang J.Y. Globally exponential stability of neural networks with variable delays. IEEE Transactions on Circuits and Systems Part I 2003, 50(2):288-291.
    • (2003) IEEE Transactions on Circuits and Systems Part I , vol.50 , Issue.2 , pp. 288-291
    • Zhang, J.Y.1
  • 53
    • 6344254943 scopus 로고    scopus 로고
    • Delay-dependent exponential stability of cellular neural networks with time-varying delays
    • Zhang Q. Delay-dependent exponential stability of cellular neural networks with time-varying delays. Chaos, Solitons and Fractals 2005, 23:1361-1369.
    • (2005) Chaos, Solitons and Fractals , vol.23 , pp. 1361-1369
    • Zhang, Q.1
  • 54
    • 34248655704 scopus 로고    scopus 로고
    • Global asymptotic stability of delayed cellular neural networks
    • Zhang H., Wang Z. Global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks 2007, 18(3):947-950.
    • (2007) IEEE Transactions on Neural Networks , vol.18 , Issue.3 , pp. 947-950
    • Zhang, H.1    Wang, Z.2
  • 55
    • 44349110244 scopus 로고    scopus 로고
    • Global asymptotic stability of recurrent neural networks with multiple time-varying delays
    • Zhang H., Wang Z., Liu D. Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Transactions on Neural Networks 2008, 19(5):855-873.
    • (2008) IEEE Transactions on Neural Networks , vol.19 , Issue.5 , pp. 855-873
    • Zhang, H.1    Wang, Z.2    Liu, D.3
  • 56
    • 3142600873 scopus 로고    scopus 로고
    • An analysis on the global asymptotic stability for neural networks with variable delays
    • Zhang Q., Wei X., Xu J. An analysis on the global asymptotic stability for neural networks with variable delays. Physics Letters A 2004, 328:163-169.
    • (2004) Physics Letters A , vol.328 , pp. 163-169
    • Zhang, Q.1    Wei, X.2    Xu, J.3
  • 57
    • 33746011594 scopus 로고    scopus 로고
    • Stability of delayed cellular neural networks
    • Zhang Q., Wei X., Xu J. Stability of delayed cellular neural networks. Chaos, Solitons and Fractals 2007, 31(31):514-520.
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.31 , pp. 514-520
    • Zhang, Q.1    Wei, X.2    Xu, J.3
  • 58
    • 0037174277 scopus 로고    scopus 로고
    • Globally exponential stability conditions for cellular neural networks with time-varying delays
    • Zhou D.M., Cao J.D. Globally exponential stability conditions for cellular neural networks with time-varying delays. Applied Mathematics and Computation 2002, 131(2-3):487-496.
    • (2002) Applied Mathematics and Computation , vol.131 , Issue.2-3 , pp. 487-496
    • Zhou, D.M.1    Cao, J.D.2


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