메뉴 건너뛰기




Volumn 53, Issue 1-2, 2000, Pages 1-39

Dynamics of a class of discrete-time neural networks and their continuous-time counterparts

Author keywords

Continuous time models; Discrete time models; Global exponential asymptotic stability; Neural networks with time delays; Numerical solutions

Indexed keywords


EID: 0013046313     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(00)00168-3     Document Type: Article
Times cited : (176)

References (46)
  • 2
    • 0026899601 scopus 로고
    • Stability of fixed points and periodic orbits and bifurcations in analog networks
    • E.K. Blum, X. Wang, Stability of fixed points and periodic orbits and bifurcations in analog networks, Neural Networks 5 (1992) 577-587.
    • (1992) Neural Networks , vol.5 , pp. 577-587
    • Blum, E.K.1    Wang, X.2
  • 4
    • 0032298907 scopus 로고    scopus 로고
    • Global attractivity in delayed Hopfield neural network models
    • P. van den Driessche, X. Zou, Global attractivity in delayed Hopfield neural network models, SIAM J. Appl. Math. 58 (1998) 1878-1890.
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1878-1890
    • Van Den Driessche, P.1    Zou, X.2
  • 6
    • 0030194344 scopus 로고    scopus 로고
    • Stability analysis of dynamical neural networks
    • Y. Fang, G. Kincaid, Stability analysis of dynamical neural networks, IEEE Trans. Neural Networks 7 (1996) 996-1006.
    • (1996) IEEE Trans. Neural Networks , vol.7 , pp. 996-1006
    • Fang, Y.1    Kincaid, G.2
  • 7
    • 43949155364 scopus 로고
    • On global asymptotic stability of a class of nonlinear systems arising in neural network theory
    • M. Forti, On global asymptotic stability of a class of nonlinear systems arising in neural network theory, J. Differential Eqns. 113 (1994) 246-264.
    • (1994) J. Differential Eqns. , vol.113 , pp. 246-264
    • Forti, M.1
  • 8
    • 0026883588 scopus 로고
    • A condition for global convergence of a class of symmetric neural circuits
    • M. Forti, S. Manetti, M. Marini, A condition for global convergence of a class of symmetric neural circuits, IEEE Trans. Circuits Syst. 39 (1992) 480-483.
    • (1992) IEEE Trans. Circuits Syst. , vol.39 , pp. 480-483
    • Forti, M.1    Manetti, S.2    Marini, M.3
  • 9
    • 0028465673 scopus 로고
    • Necessary and sufficient condition for absolute stability of neural networks
    • M. Forti, S. Manetti, M. Marini, Necessary and sufficient condition for absolute stability of neural networks, IEEE Trans. Circuits Syst. 41 (1994) 491-494.
    • (1994) IEEE Trans. Circuits Syst. , vol.41 , pp. 491-494
    • Forti, M.1    Manetti, S.2    Marini, M.3
  • 10
    • 0001075269 scopus 로고
    • Stability in asymmetric Hopfield nets with transmission delays
    • K. Gopalsamy, X.Z. He, Stability in asymmetric Hopfield nets with transmission delays, Physica D 76 (1994) 344-358.
    • (1994) Physica D , vol.76 , pp. 344-358
    • Gopalsamy, K.1    He, X.Z.2
  • 12
    • 0000454723 scopus 로고
    • D.F. Griffiths, P.K. Sweby, H.C. Yee, On spurious asymptotic numerical solutions of explicit Runge-Kutta methods, in: Proceedings of the EMA Conference on Dynamics of Numerics and Numerics of Dynamics, Bristol, 1990, IMA J. Numer. Anal. 12 (1992) 319-338.
    • (1992) IMA J. Numer. Anal. , vol.12 , pp. 319-338
  • 15
    • 0024909476 scopus 로고
    • Convergent activation dynamics in continuous time networks
    • M.W. Hirsch, Convergent activation dynamics in continuous time networks, Neural Networks 2 (1989) 331-349.
    • (1989) Neural Networks , vol.2 , pp. 331-349
    • Hirsch, M.W.1
  • 16
    • 0020118274 scopus 로고
    • Neural networks and physical systems with collective computational abilities
    • J.J. Hopfield, Neural networks and physical systems with collective computational abilities, Proc. Natl. Acad. Sci. USA 79 (1982) 2554-2558.
    • (1982) Proc. Natl. Acad. Sci. USA , vol.79 , pp. 2554-2558
    • Hopfield, J.J.1
  • 17
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like those of two-state neurons
    • J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA 81 (1984) 3088-3092.
    • (1984) Proc. Natl. Acad. Sci. USA , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 18
    • 0022504321 scopus 로고
    • Computing with neural circuits: A model
    • J.J. Hopfield, D.W. Tank, Computing with neural circuits: A model, Science 233 (1986) 625-633.
    • (1986) Science , vol.233 , pp. 625-633
    • Hopfield, J.J.1    Tank, D.W.2
  • 19
    • 0002959217 scopus 로고
    • Stability and dynamics of numerical methods for nonlinear ordinary differential equations
    • A. Iserles, Stability and dynamics of numerical methods for nonlinear ordinary differential equations, IMA J. Numer. Anal. 10 (1990) 1-30.
    • (1990) IMA J. Numer. Anal. , vol.10 , pp. 1-30
    • Iserles, A.1
  • 20
    • 0002869551 scopus 로고
    • An optimization network for matrix inversion
    • D.Z. Anderson (Ed.), American Institute of Physics, New York
    • J. Jang, S. Lee, S. Shin, An optimization network for matrix inversion, in: D.Z. Anderson (Ed.), Neural Information Processing Systems, American Institute of Physics, New York, 1988, pp. 397-401.
    • (1988) Neural Information Processing Systems , pp. 397-401
    • Jang, J.1    Lee, S.2    Shin, S.3
  • 21
    • 0030193060 scopus 로고    scopus 로고
    • Globally asymptotical stability of discrete time analog neural networks
    • L. Jin, M.M. Gupta, Globally asymptotical stability of discrete time analog neural networks, IEEE Trans. Neural Networks 7 (1996) 1024-1031.
    • (1996) IEEE Trans. Neural Networks , vol.7 , pp. 1024-1031
    • Jin, L.1    Gupta, M.M.2
  • 22
    • 0025405546 scopus 로고
    • Stability in contractive nonlinear neural networks
    • D.G. Kelly, Stability in contractive nonlinear neural networks, IEEE Trans. Biomed. Eng. 37 (1990) 231-242.
    • (1990) IEEE Trans. Biomed. Eng. , vol.37 , pp. 231-242
    • Kelly, D.G.1
  • 23
    • 0026932163 scopus 로고
    • Asymptotic stability of discrete time systems with saturation nonlinearities with applications to digital filters
    • D. Liu, A.N. Michel, Asymptotic stability of discrete time systems with saturation nonlinearities with applications to digital filters, IEEE Trans. Circuits Syst. I 39 (1992) 798-807.
    • (1992) IEEE Trans. Circuits Syst. I , vol.39 , pp. 798-807
    • Liu, D.1    Michel, A.N.2
  • 24
    • 0000256610 scopus 로고
    • Stability of analog neural networks with delay
    • C.M. Marcus, R.M. Westervelt, Stability of analog neural networks with delay, Phys. Rev. A 39 (1989) 347-359.
    • (1989) Phys. Rev. A , vol.39 , pp. 347-359
    • Marcus, C.M.1    Westervelt, R.M.2
  • 25
    • 0026679036 scopus 로고
    • Stability conditions for nonlinear continuous neural networks with asymmetric connection weights
    • K. Matsuoka, Stability conditions for nonlinear continuous neural networks with asymmetric connection weights, Neural Networks 5 (1992) 495-500.
    • (1992) Neural Networks , vol.5 , pp. 495-500
    • Matsuoka, K.1
  • 26
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • R.M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976) 459-467.
    • (1976) Nature , vol.261 , pp. 459-467
    • May, R.M.1
  • 30
    • 0027148066 scopus 로고
    • Associative memory with non-monotone dynamics
    • M. Morita, Associative memory with non-monotone dynamics, Neural Networks 6 (1993) 115-126.
    • (1993) Neural Networks , vol.6 , pp. 115-126
    • Morita, M.1
  • 31
    • 0002713135 scopus 로고
    • Exact solution of a difference approximation to Duffing's equation
    • R.B. Potts, Exact solution of a difference approximation to Duffing's equation, J. Aust. Math. Soc. Ser. B 23 (1981) 64-77.
    • (1981) J. Aust. Math. Soc. Ser. B , vol.23 , pp. 64-77
    • Potts, R.B.1
  • 32
    • 0000417754 scopus 로고
    • Best difference equation approximation to Buffing's equation
    • R.B. Potts, Best difference equation approximation to Buffing's equation, J. Aust. Math. Soc. Ser. B 23 (1982) 349-456.
    • (1982) J. Aust. Math. Soc. Ser. B , vol.23 , pp. 349-456
    • Potts, R.B.1
  • 33
    • 0000258580 scopus 로고
    • Differential and difference equations
    • R.B. Potts, Differential and difference equations, Am. Math. Monthly 89 (1982) 402-407.
    • (1982) Am. Math. Monthly , vol.89 , pp. 402-407
    • Potts, R.B.1
  • 35
    • 0022011947 scopus 로고
    • Turbulence in multistep methods for initial value problems
    • M. Prufer, Turbulence in multistep methods for initial value problems, SIAM J. Appl. Math. 45 (1985) 32-69.
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 32-69
    • Prufer, M.1
  • 36
    • 0001947933 scopus 로고
    • Warning-handle with care
    • I. Stewart, Warning-handle with care, Nature 355 (1992) 16-17.
    • (1992) Nature , vol.355 , pp. 16-17
    • Stewart, I.1
  • 37
    • 0022721216 scopus 로고
    • Simple neural optimization networks: An A/D converter, signal decision circuit and a linear programming circuit
    • D.W. Tank, J.J. Hopfield, Simple neural optimization networks: An A/D converter, signal decision circuit and a linear programming circuit, IEEE Trans. Circuits Syst. 33 (1986) 533-541.
    • (1986) IEEE Trans. Circuits Syst. , vol.33 , pp. 533-541
    • Tank, D.W.1    Hopfield, J.J.2
  • 38
    • 0000644645 scopus 로고
    • Central difference scheme and chaos
    • S. Ushiki, Central difference scheme and chaos, Physica D 4 (1982) 407-424.
    • (1982) Physica D , vol.4 , pp. 407-424
    • Ushiki, S.1
  • 39
    • 0026900945 scopus 로고
    • Discrete-time versus continuous-time models of neural networks
    • X. Wang, E.K. Blum, Discrete-time versus continuous-time models of neural networks, J. Comput. Syst. Sci. 45 (1992) 1-19.
    • (1992) J. Comput. Syst. Sci. , vol.45 , pp. 1-19
    • Wang, X.1    Blum, E.K.2
  • 40
    • 0040115229 scopus 로고
    • Euler's finite difference scheme and chaos
    • M. Yamaguti, H. Matano, Euler's finite difference scheme and chaos, Proc. Jpn. Acad. 55 (1979) 78-80.
    • (1979) Proc. Jpn. Acad. , vol.55 , pp. 78-80
    • Yamaguti, M.1    Matano, H.2
  • 41
    • 0001650860 scopus 로고
    • Chaos in numerical analysis of ordinary differential equations
    • M. Yamaguti, S. Ushiki, Chaos in numerical analysis of ordinary differential equations, Physica D 3 (1981) 618-626.
    • (1981) Physica D , vol.3 , pp. 618-626
    • Yamaguti, M.1    Ushiki, S.2
  • 42
    • 0028497220 scopus 로고
    • Exponential stability and oscillation of Hopfield graded response neural networks
    • H. Yang, T.S. Dillon, Exponential stability and oscillation of Hopfield graded response neural networks, IEEE Trans. Neural Networks 5 (1994) 719-729.
    • (1994) IEEE Trans. Neural Networks , vol.5 , pp. 719-729
    • Yang, H.1    Dillon, T.S.2
  • 43
    • 0000791959 scopus 로고
    • Global stability and local stability of Hopfield neural networks with delays
    • H. Ye, A.N. Michel, K. Wang, 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
  • 44
    • 0010528967 scopus 로고
    • A study of spurious asymptotic numerical solutions of nonlinear differential equations by the nonlinear dynamics approach
    • Proceedings of the 12th International Conference on Numerical Methods in Fluid Dynamics, Oxford, Springer, Berlin, 1990
    • H.C. Yee, P.K. Sweby, D.F. Griffiths, A study of spurious asymptotic numerical solutions of nonlinear differential equations by the nonlinear dynamics approach, in: Lecture Notes in Physics, Vol. 371, Proceedings of the 12th International Conference on Numerical Methods in Fluid Dynamics, Oxford, 1992, Springer, Berlin, 1990, pp. 259-267.
    • (1992) Lecture Notes in Physics , vol.371 , pp. 259-267
    • Yee, H.C.1    Sweby, P.K.2    Griffiths, D.F.3
  • 45
    • 3042829361 scopus 로고
    • Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I. the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics
    • H.C. Yee, P.K. Sweby, D.F. Griffiths, Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I. The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics, J. Comput. Phys. 97 (1991) 249-310.
    • (1991) J. Comput. Phys. , vol.97 , pp. 249-310
    • Yee, H.C.1    Sweby, P.K.2    Griffiths, D.F.3
  • 46
    • 0027224451 scopus 로고
    • Capacity of associative memory using a nonmonotonic neuron model
    • S. Yoshizawa, M. Morita, S. Amari, Capacity of associative memory using a nonmonotonic neuron model, Neural Networks 6 (1993) 167-176.
    • (1993) Neural Networks , vol.6 , pp. 167-176
    • Yoshizawa, S.1    Morita, M.2    Amari, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.