메뉴 건너뛰기




Volumn 33, Issue , 2012, Pages 97-113

On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions

Author keywords

Convergence in finite time; Discontinuous neuron activation; Global exponential stability; Periodic solution; Time varying delayed neural networks; Topological degree theory

Indexed keywords

CONVERGENCE IN FINITE TIME; GLOBAL EXPONENTIAL STABILITY; PERIODIC SOLUTION; TIME-VARYING DELAYED; TOPOLOGICAL DEGREE THEORY;

EID: 84863876288     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2012.04.009     Document Type: Article
Times cited : (64)

References (54)
  • 1
    • 77954565406 scopus 로고    scopus 로고
    • Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks
    • Allegretto W., Papini D., Forti M. Common asymptotic behavior of solutions and almost periodicity for discontinuous, delayed, and impulsive neural networks. IEEE Transactions on Neural Networks 2010, 21(7):1110-1125.
    • (2010) IEEE Transactions on Neural Networks , vol.21 , Issue.7 , pp. 1110-1125
    • Allegretto, W.1    Papini, D.2    Forti, M.3
  • 6
    • 80052956138 scopus 로고    scopus 로고
    • Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations
    • Cai Z.W., Huang L.H. Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations. Neurocomputing 2011, 74:3170-3179.
    • (2011) Neurocomputing , vol.74 , pp. 3170-3179
    • Cai, Z.W.1    Huang, L.H.2
  • 7
    • 0037216976 scopus 로고    scopus 로고
    • Global asymptotic stability of a general class of recurrent neural networks with time-varying delays
    • Cao J.D., Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits Systems I 2003, 50(1):34-44.
    • (2003) IEEE Transactions on Circuits Systems I , vol.50 , Issue.1 , pp. 34-44
    • Cao, J.D.1    Wang, J.2
  • 8
    • 78649933705 scopus 로고    scopus 로고
    • Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations
    • Chen X.F., Song Q.K. Global exponential stability of the periodic solution of delayed Cohen-Grossberg neural networks with discontinuous activations. Neurocomputing 2010, 73:3097-3104.
    • (2010) Neurocomputing , vol.73 , pp. 3097-3104
    • Chen, X.F.1    Song, Q.K.2
  • 11
    • 0003608428 scopus 로고
    • Differential equations with discontinuous right-hand sides
    • Kluwer Academic Publishers, Boston
    • Filippov A.F. Differential equations with discontinuous right-hand sides. Mathematics and its applications (Soviet Series) 1988, Kluwer Academic Publishers, Boston.
    • (1988) Mathematics and its applications (Soviet Series)
    • Filippov, A.F.1
  • 12
    • 31144460192 scopus 로고    scopus 로고
    • Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations
    • Forti M., Grazzini M., Nistri P., Pancioni L. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Physica D 2006, 214:88-89.
    • (2006) Physica D , vol.214 , pp. 88-89
    • Forti, M.1    Grazzini, M.2    Nistri, P.3    Pancioni, L.4
  • 13
    • 0242696111 scopus 로고    scopus 로고
    • Global convergence of neural networks with discontinuous neuron activations
    • Forti M., Nistri P. Global convergence of neural networks with discontinuous neuron activations. IEEE Transactions on Circuits Systems I 2003, 50(11):1421-1435.
    • (2003) IEEE Transactions on Circuits Systems I , vol.50 , Issue.11 , pp. 1421-1435
    • Forti, M.1    Nistri, P.2
  • 14
    • 28244452021 scopus 로고    scopus 로고
    • Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain
    • Forti M., Nistri P., Papini D. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Transactions on Neural Networks 2005, 16(6):1449-1463.
    • (2005) IEEE Transactions on Neural Networks , vol.16 , Issue.6 , pp. 1449-1463
    • Forti, M.1    Nistri, P.2    Papini, D.3
  • 17
    • 67349135259 scopus 로고    scopus 로고
    • Generalized Lyapunov method for discontinuous systems
    • Guo Z.Y., Huang L.H. Generalized Lyapunov method for discontinuous systems. Nonlinear Analysis 2009, 71:3083-3092.
    • (2009) Nonlinear Analysis , vol.71 , pp. 3083-3092
    • Guo, Z.Y.1    Huang, L.H.2
  • 18
    • 38149066040 scopus 로고    scopus 로고
    • Stability analysis for neural networks with time-varying interval delay
    • He Y., Liu G.P., Rees D., Wu M. Stability analysis for neural networks with time-varying interval delay. IEEE Transactions on Neural Networks 2007, 18(6):1850-1854.
    • (2007) IEEE Transactions on Neural Networks , vol.18 , Issue.6 , pp. 1850-1854
    • He, Y.1    Liu, G.P.2    Rees, D.3    Wu, M.4
  • 19
    • 0031672895 scopus 로고    scopus 로고
    • Stability analysis for neural dynamics with time-varying delays
    • Hou C.H., Qian J.X. Stability analysis for neural dynamics with time-varying delays. IEEE Transactions on Neural Networks 1998, 9(1):221-223.
    • (1998) IEEE Transactions on Neural Networks , vol.9 , Issue.1 , pp. 221-223
    • Hou, C.H.1    Qian, J.X.2
  • 20
    • 67650805595 scopus 로고    scopus 로고
    • Global convergence of periodic solution of neural networks with discontinuous activation functions
    • Huang L.H., Guo Z.Y. Global convergence of periodic solution of neural networks with discontinuous activation functions. Chaos, Solitons and Fractals 2009, 42:2351-2356.
    • (2009) Chaos, Solitons and Fractals , vol.42 , pp. 2351-2356
    • Huang, L.H.1    Guo, Z.Y.2
  • 22
    • 20444396501 scopus 로고    scopus 로고
    • Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays
    • Huang H., Ho D.W.C., Lam J. Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Transactions on Circuits Systems II 2005, 52(5):251-255.
    • (2005) IEEE Transactions on Circuits Systems II , vol.52 , Issue.5 , pp. 251-255
    • Huang, H.1    Ho, D.W.C.2    Lam, J.3
  • 23
    • 60549087956 scopus 로고    scopus 로고
    • Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations
    • Huang L.H., Wang J.F., Zhou X.N. Existence and global asymptotic stability of periodic solutions for Hopfield neural networks with discontinuous activations. Nonlinear Analysis. Real World Applications 2009, 10:1651-1661.
    • (2009) Nonlinear Analysis. Real World Applications , vol.10 , pp. 1651-1661
    • Huang, L.H.1    Wang, J.F.2    Zhou, X.N.3
  • 24
    • 33644898137 scopus 로고    scopus 로고
    • Polychronization: computation with spikes
    • Izhikevich E.M. Polychronization: computation with spikes. Neural Computation 2006, 18:245-282.
    • (2006) Neural Computation , vol.18 , pp. 245-282
    • Izhikevich, E.M.1
  • 25
    • 0036890845 scopus 로고    scopus 로고
    • A fast learning algorithm for time-delay neural networks
    • Jiang M., Gielen G., Deng B., Zhu X. A fast learning algorithm for time-delay neural networks. Information Sciences 2002, 148:27-39.
    • (2002) Information Sciences , vol.148 , pp. 27-39
    • Jiang, M.1    Gielen, G.2    Deng, B.3    Zhu, X.4
  • 27
    • 77952542217 scopus 로고    scopus 로고
    • Delayed Lagrangian neural networks for solving convex programming problems
    • Li F. Delayed Lagrangian neural networks for solving convex programming problems. Neurocomputing 2010, 73:2266-2273.
    • (2010) Neurocomputing , vol.73 , pp. 2266-2273
    • Li, F.1
  • 28
    • 24044465139 scopus 로고    scopus 로고
    • Global asymptotic stability and global exponential stability of delayed cellular neural networks
    • Liao X.X., Wang J., Zeng Z.G. Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Transactions on Circuits Systems II 2005, 52(7):403-409.
    • (2005) IEEE Transactions on Circuits Systems II , vol.52 , Issue.7 , pp. 403-409
    • Liao, X.X.1    Wang, J.2    Zeng, Z.G.3
  • 30
    • 67349181808 scopus 로고    scopus 로고
    • On periodic solutions of neural networks via differential inclusions
    • Liu X.Y., Cao J.D. On periodic solutions of neural networks via differential inclusions. Neural Networks 2009, 22:329-334.
    • (2009) Neural Networks , vol.22 , pp. 329-334
    • Liu, X.Y.1    Cao, J.D.2
  • 31
    • 79953207030 scopus 로고    scopus 로고
    • Robust state estimations for neural networks with discontinuous activations
    • Liu X.Y., Cao J.D. Robust state estimations for neural networks with discontinuous activations. IEEE Transactions on Systems, Man, and Cybernetics-Part B 2010, 40(6):1425-1437.
    • (2010) IEEE Transactions on Systems, Man, and Cybernetics-Part B , vol.40 , Issue.6 , pp. 1425-1437
    • Liu, X.Y.1    Cao, J.D.2
  • 32
    • 80054787200 scopus 로고    scopus 로고
    • Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches
    • Liu X.Y., Chen T.P., Cao J.D., Lu W.L. Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Networks 2011, 24:1013-1021.
    • (2011) Neural Networks , vol.24 , pp. 1013-1021
    • Liu, X.Y.1    Chen, T.P.2    Cao, J.D.3    Lu, W.L.4
  • 33
    • 80055058410 scopus 로고    scopus 로고
    • Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations
    • Liu J., Liu X.Z., Xie W.C. Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations. Information Sciences 2012, 183:92-105.
    • (2012) Information Sciences , vol.183 , pp. 92-105
    • Liu, J.1    Liu, X.Z.2    Xie, W.C.3
  • 35
    • 19344378953 scopus 로고    scopus 로고
    • Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions
    • Lu W.L., Chen T.P. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Networks 2005, 18(3):231-242.
    • (2005) Neural Networks , vol.18 , Issue.3 , pp. 231-242
    • Lu, W.L.1    Chen, T.P.2
  • 36
    • 33645706718 scopus 로고    scopus 로고
    • Dynamical behaviors of delayed neural networks systems with discontinuous activation functions
    • Lu W.L., Chen T.P. Dynamical behaviors of delayed neural networks systems with discontinuous activation functions. Neural Computation 2006, 18:683-708.
    • (2006) Neural Computation , vol.18 , pp. 683-708
    • Lu, W.L.1    Chen, T.P.2
  • 37
    • 41849114189 scopus 로고    scopus 로고
    • Almost periodic dynamics of a class of delayed neural networks with discontinuous activations
    • Lu W.L., Chen T.P. Almost periodic dynamics of a class of delayed neural networks with discontinuous activations. Neural Computation 2008, 20:1065-1090.
    • (2008) Neural Computation , vol.20 , pp. 1065-1090
    • Lu, W.L.1    Chen, T.P.2
  • 38
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • Marcus C.M., Westervelt R.M. Stability of analog neural networks with delay. Physical Review A 1989, 39:347-359.
    • (1989) Physical Review A , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 39
    • 84857203488 scopus 로고    scopus 로고
    • Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions
    • Nie X.B., Cao J.D. Existence and global stability of equilibrium point for delayed competitive neural networks with discontinuous activation functions. International Journal of Systems Science 2012, 43(3):459-474.
    • (2012) International Journal of Systems Science , vol.43 , Issue.3 , pp. 459-474
    • Nie, X.B.1    Cao, J.D.2
  • 40
    • 23244467962 scopus 로고    scopus 로고
    • Finite time stability and robust control synthesis of uncertain switched systems
    • Orlov Y. Finite time stability and robust control synthesis of uncertain switched systems. SIAM Journal on Control and Optimization 2005, 43:1253-1271.
    • (2005) SIAM Journal on Control and Optimization , vol.43 , pp. 1253-1271
    • Orlov, Y.1
  • 41
    • 21744455449 scopus 로고    scopus 로고
    • Global exponential stability of the periodic solution of a delayed neural networks with discontinuous activations
    • Papini D., Taddei V. Global exponential stability of the periodic solution of a delayed neural networks with discontinuous activations. Physics Letters A 2005, 343:117-128.
    • (2005) Physics Letters A , vol.343 , pp. 117-128
    • Papini, D.1    Taddei, V.2
  • 42
    • 67649088057 scopus 로고    scopus 로고
    • Global exponential stability and global convergence in finite time of neural networks with discontinuous activations
    • Qin S.T., Xue X.P. Global exponential stability and global convergence in finite time of neural networks with discontinuous activations. Neural Processing Letters 2009, 29:189-204.
    • (2009) Neural Processing Letters , vol.29 , pp. 189-204
    • Qin, S.T.1    Xue, X.P.2
  • 43
    • 57649097481 scopus 로고    scopus 로고
    • Dynamical behaviors of delayed Hopfield neural networks with discontinuous activations
    • Wang J.F., Huang L.H., Guo Z.Y. Dynamical behaviors of delayed Hopfield neural networks with discontinuous activations. Applied Mathematical Modelling 2009, 33:1793-1802.
    • (2009) Applied Mathematical Modelling , vol.33 , pp. 1793-1802
    • Wang, J.F.1    Huang, L.H.2    Guo, Z.Y.3
  • 44
    • 0030215775 scopus 로고    scopus 로고
    • Stability analysis of differential inclusions in Banach space with applications to nonlinear systems with time delays
    • Wang K.L., Michel A.N. Stability analysis of differential inclusions in Banach space with applications to nonlinear systems with time delays. IEEE Transactions on Circuits and Systems I 1996, 43:617-626.
    • (1996) IEEE Transactions on Circuits and Systems I , vol.43 , pp. 617-626
    • Wang, K.L.1    Michel, A.N.2
  • 45
    • 60549088323 scopus 로고    scopus 로고
    • Stability analysis for periodic solution of neural networks with discontinuous neuron activations
    • Wu H.Q. Stability analysis for periodic solution of neural networks with discontinuous neuron activations. Nonlinear Analysis. Real World Applications 2009, 10:1717-1729.
    • (2009) Nonlinear Analysis. Real World Applications , vol.10 , pp. 1717-1729
    • Wu, H.Q.1
  • 46
    • 51049120067 scopus 로고    scopus 로고
    • Existence and stability of periodic solution for BAM neural networks with discontinuous neuron activations
    • Wu H.Q., Li Y.W. Existence and stability of periodic solution for BAM neural networks with discontinuous neuron activations. Computers and Mathematics with Applications 2008, 56:1981-1993.
    • (2008) Computers and Mathematics with Applications , vol.56 , pp. 1981-1993
    • Wu, H.Q.1    Li, Y.W.2
  • 47
  • 48
    • 77649233055 scopus 로고    scopus 로고
    • Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays
    • Wu X.R., Wang Y.N., Huang L.H., Zuo Y. Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays. Neurocomputing 2010, 73:1265-1271.
    • (2010) Neurocomputing , vol.73 , pp. 1265-1271
    • Wu, X.R.1    Wang, Y.N.2    Huang, L.H.3    Zuo, Y.4
  • 50
    • 77955513608 scopus 로고    scopus 로고
    • Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function
    • Zeng Z.G., Huang T.W., Zheng W.X. Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Transactions on Neural Networks 2010, 21(8):1371-1377.
    • (2010) IEEE Transactions on Neural Networks , vol.21 , Issue.8 , pp. 1371-1377
    • Zeng, Z.G.1    Huang, T.W.2    Zheng, W.X.3
  • 51
    • 0142165161 scopus 로고    scopus 로고
    • Global exponential stability of a general class of recurrent neural networks with time-varying delays
    • Zeng Z.G., Wang J., Liao X.X. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits Systems I 2003, 50(10):1353-1358.
    • (2003) IEEE Transactions on Circuits Systems I , vol.50 , Issue.10 , pp. 1353-1358
    • Zeng, Z.G.1    Wang, J.2    Liao, X.X.3
  • 52
    • 73949132376 scopus 로고    scopus 로고
    • Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay
    • Zhang H.G., Liu Z.W., Huang G.B., Wang Z.S. Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Transactions on Neural Networks 2010, 21(1):91-106.
    • (2010) IEEE Transactions on Neural Networks , vol.21 , Issue.1 , pp. 91-106
    • Zhang, H.G.1    Liu, Z.W.2    Huang, G.B.3    Wang, Z.S.4
  • 53
    • 37249058833 scopus 로고    scopus 로고
    • Global exponential convergence of time-varying delayed neural networks with high gain
    • Zhang L., Yi Z. Global exponential convergence of time-varying delayed neural networks with high gain. Lecture Notes in Computer Science 2007, 4491:1005-1011.
    • (2007) Lecture Notes in Computer Science , vol.4491 , pp. 1005-1011
    • Zhang, L.1    Yi, Z.2
  • 54
    • 60449086840 scopus 로고    scopus 로고
    • Robust stability criterion for delayed neural networks with discontinuous activation functions
    • Zuo Y., Wang Y.N., Huang L.H., Wang Z.Y., Liu X.Z., Wu X.R. Robust stability criterion for delayed neural networks with discontinuous activation functions. Neural Processing Letters 2009, 29:29-44.
    • (2009) Neural Processing Letters , vol.29 , pp. 29-44
    • Zuo, Y.1    Wang, Y.N.2    Huang, L.H.3    Wang, Z.Y.4    Liu, X.Z.5    Wu, X.R.6


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.