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Volumn 164, Issue 2, 2000, Pages 431-450

Existence and Multiplicity of Traveling Waves in a Lattice Dynamical System

Author keywords

Cellular neural networks; Discrete dynamical system; Traveling wave

Indexed keywords


EID: 0000425056     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3770     Document Type: Article
Times cited : (49)

References (38)
  • 1
    • 21844518397 scopus 로고
    • Chaos of traveling waves in a discrete chain of diffusively coupled maps
    • Afraimovich V. S., Nekorin V. I. Chaos of traveling waves in a discrete chain of diffusively coupled maps. Internat. J. Bifurcation Chaos. 4:1994;631-637.
    • (1994) Internat. J. Bifurcation Chaos , vol.4 , pp. 631-637
    • Afraimovich, V.S.1    Nekorin, V.I.2
  • 2
    • 0019582693 scopus 로고
    • Some threshold results for models of myelinated nerves
    • Bell J. Some threshold results for models of myelinated nerves. Math. Biosciences. 54:1981;181-190.
    • (1981) Math. Biosciences , vol.54 , pp. 181-190
    • Bell, J.1
  • 3
    • 0021408619 scopus 로고
    • Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons
    • Bell J., Cosner C. Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons. Quart. Appl. Math. 42:1984;1-14.
    • (1984) Quart. Appl. Math. , vol.42 , pp. 1-14
    • Bell, J.1    Cosner, C.2
  • 4
    • 6244279498 scopus 로고
    • Theory of crystal growth and interface motion in crystalline materials
    • Cahn J. W. Theory of crystal growth and interface motion in crystalline materials. Acta Metallurgica. 8:1960;554-562.
    • (1960) Acta Metallurgica , vol.8 , pp. 554-562
    • Cahn, J.W.1
  • 6
    • 0032201919 scopus 로고    scopus 로고
    • Traveling wave solutions for systems of ODE's on a two-dimensional spatial lattice
    • Cahn J. W., Mallet-Paret J., Van Vleck E. S. Traveling wave solutions for systems of ODE's on a two-dimensional spatial lattice. SIAM J. Appl. Math. 59:1998;455-493.
    • (1998) SIAM J. Appl. Math. , vol.59 , pp. 455-493
    • Cahn, J.W.1    Mallet-Paret, J.2    Van Vleck, E.S.3
  • 7
    • 0001868062 scopus 로고
    • Transition layers for singular perturbed delay differential equations with monotone nonlinearities
    • Chow S.-N., Lin X. B., Mallet-Paret J. Transition layers for singular perturbed delay differential equations with monotone nonlinearities. J. Dynam. Differential Equations. 1:1989;3-43.
    • (1989) J. Dynam. Differential Equations , vol.1 , pp. 3-43
    • Chow, S.-N.1    Lin, X.B.2    Mallet-Paret, J.3
  • 8
    • 0000253503 scopus 로고    scopus 로고
    • Pattern formation and spatial chaos in spatially discrete evolution equations
    • Chow S.-N., Mallet-Paret J., Van Vleck E. S. Pattern formation and spatial chaos in spatially discrete evolution equations. Random Comput. Dynamics. 4:1996;109-178.
    • (1996) Random Comput. Dynamics , vol.4 , pp. 109-178
    • Chow, S.-N.1    Mallet-Paret, J.2    Van Vleck, E.S.3
  • 10
    • 0003170927 scopus 로고
    • Stability and bifurcation of traveling wave solutions in coupled map lattices
    • Chow S.-N., Shen W. Stability and bifurcation of traveling wave solutions in coupled map lattices. J. Dynamical Systems Appl. 4:1995;1-26.
    • (1995) J. Dynamical Systems Appl. , vol.4 , pp. 1-26
    • Chow, S.-N.1    Shen, W.2
  • 14
    • 43949163245 scopus 로고
    • Propagation waves in discrete bistable reaction-diffusion systems
    • Erneux T., Nicolis G. Propagation waves in discrete bistable reaction-diffusion systems. Physica D. 67:1993;237-244.
    • (1993) Physica D , vol.67 , pp. 237-244
    • Erneux, T.1    Nicolis, G.2
  • 15
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to traveling front solutions
    • Fife P., McLeod J. The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch. Rational Mech. Anal. 65:1977;333-361.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 333-361
    • Fife, P.1    McLeod, J.2
  • 18
    • 0000254825 scopus 로고
    • Wavefronts for cooperative tridigonal system of differential equations
    • Hankerson D., Zinner B. Wavefronts for cooperative tridigonal system of differential equations. J. Dynam. Differential Equations. 5:1993;359-373.
    • (1993) J. Dynam. Differential Equations , vol.5 , pp. 359-373
    • Hankerson, D.1    Zinner, B.2
  • 19
    • 0033164105 scopus 로고    scopus 로고
    • Traveling waves in cellular neural networks
    • Hsu C.-H., Lin S. S. Traveling waves in cellular neural networks. Int. J. Bifurcation and Chaos. 9:1999;1307-1319.
    • (1999) Int. J. Bifurcation and Chaos , vol.9 , pp. 1307-1319
    • Hsu, C.-H.1    Lin, S.S.2
  • 20
    • 0141901882 scopus 로고
    • Existence of traveling waves for a generalized discrete Fisher's equations
    • Hudson H., Zinner B. Existence of traveling waves for a generalized discrete Fisher's equations. Comm. Appl. Nonlinear Anal. 1:1994;23-46.
    • (1994) Comm. Appl. Nonlinear Anal. , vol.1 , pp. 23-46
    • Hudson, H.1    Zinner, B.2
  • 21
    • 0033723714 scopus 로고    scopus 로고
    • Cellular neural networks: Mosaic pattern and spatial chaos
    • Juang J., Lin S. S. Cellular neural networks: mosaic pattern and spatial chaos. SIAM J. Appl. Math. 2000;891-915.
    • (2000) SIAM J. Appl. Math. , pp. 891-915
    • Juang, J.1    Lin, S.S.2
  • 23
    • 0023362335 scopus 로고
    • Propagation and its failure in coupled system of discrete excitable cells
    • Keener J. P. Propagation and its failure in coupled system of discrete excitable cells. SIAM J. Appl. Math. 47:1987;556-572.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 556-572
    • Keener, J.P.1
  • 24
    • 0000234351 scopus 로고
    • Propagation failure in arrays of coupled bistable chemical reactors
    • Laplante J. P., Erneux T. Propagation failure in arrays of coupled bistable chemical reactors. J. Phys. Chem. 96:1992;4931-4934.
    • (1992) J. Phys. Chem. , vol.96 , pp. 4931-4934
    • Laplante, J.P.1    Erneux, T.2
  • 26
    • 0001238052 scopus 로고    scopus 로고
    • Spatial patterns, spatial chaos, and traveling waves in lattice differential equations
    • S. J. van Strien, & S. M. Verduyn Lunel. Amsterdam: North-Holland
    • Mallet-Paret J. Spatial patterns, spatial chaos, and traveling waves in lattice differential equations. van Strien S. J., Verduyn Lunel S. M. Stochastic and Spatial Structures of Dynamical Systems. 1996;105-129 North-Holland, Amsterdam.
    • (1996) Stochastic and Spatial Structures of Dynamical Systems , pp. 105-129
    • Mallet-Paret, J.1
  • 27
    • 0001935025 scopus 로고    scopus 로고
    • The Fredholm alternative for functional differential equations of mixed type
    • Mallet-Paret J. The Fredholm alternative for functional differential equations of mixed type. J. Dynam. Differential Equations. 11:1999;1-48.
    • (1999) J. Dynam. Differential Equations , vol.11 , pp. 1-48
    • Mallet-Paret, J.1
  • 28
    • 53149083400 scopus 로고    scopus 로고
    • The global structure of traveling waves in spatial discrete dynamical systems
    • Mallet-Paret J. The global structure of traveling waves in spatial discrete dynamical systems. J. Dynam. Differential Equations. 11:1999;49-127.
    • (1999) J. Dynam. Differential Equations , vol.11 , pp. 49-127
    • Mallet-Paret, J.1
  • 29
    • 0029390406 scopus 로고
    • Pattern formation and spatial chaos in lattice dynamical systems, II
    • Mallet-Paret J., Chow S.-N. Pattern formation and spatial chaos in lattice dynamical systems, II. IEEE Trans. Circuits and Systems. 42:1995;752-756.
    • (1995) IEEE Trans. Circuits and Systems , vol.42 , pp. 752-756
    • Mallet-Paret, J.1    Chow, S.-N.2
  • 30
    • 0030102662 scopus 로고    scopus 로고
    • Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions
    • Mallet-Paret J., Sell G. R. Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions. J. Differential Equations. 125:1996;385-440.
    • (1996) J. Differential Equations , vol.125 , pp. 385-440
    • Mallet-Paret, J.1    Sell, G.R.2
  • 31
    • 0030102885 scopus 로고    scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
    • Mallet-Paret J., Sell G. R. The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay. J. Differential Equations. 125:1996;441-489.
    • (1996) J. Differential Equations , vol.125 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.R.2
  • 33
    • 0030269335 scopus 로고    scopus 로고
    • Lifted lattices, hyperbolic structures, and topological disorders in coupled map lattices
    • Shen W. Lifted lattices, hyperbolic structures, and topological disorders in coupled map lattices. SIAM J. Appl. Math. 56:1996;1379-1399.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1379-1399
    • Shen, W.1
  • 35
    • 0001651766 scopus 로고    scopus 로고
    • Asymptotical and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations
    • Wu J., Zou X. Asymptotical and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations. J. Differential Equations. 135:1997;315-357.
    • (1997) J. Differential Equations , vol.135 , pp. 315-357
    • Wu, J.1    Zou, X.2
  • 36
    • 0000334726 scopus 로고
    • Stability of traveling wavefront solutions for the discrete Nagumo equation
    • Zinner B. Stability of traveling wavefront solutions for the discrete Nagumo equation. SIAM J. Math. Anal. 22:1991;1016-1020.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1016-1020
    • Zinner, B.1
  • 37
    • 0004711956 scopus 로고
    • Existence of traveling wavefront solutions for discrete Nagumo equation
    • Zinner B. Existence of traveling wavefront solutions for discrete Nagumo equation. J. Differential Equations. 96:1992;1-27.
    • (1992) J. Differential Equations , vol.96 , pp. 1-27
    • Zinner, B.1
  • 38
    • 0002802598 scopus 로고
    • Traveling wavefronts for the discrete Fisher's equation
    • Zinner B., Harris G., Hudson W. Traveling wavefronts for the discrete Fisher's equation. J. Differential Equations. 105:1993;46-62.
    • (1993) J. Differential Equations , vol.105 , pp. 46-62
    • Zinner, B.1    Harris, G.2    Hudson, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.