Bichromatic Travelling Waves for Lattice Nagumo Equations

被引：11
|
作者：
Hupkes, Hermen Jan [1 ]
Morelli, Leonardo [1 ]
Stehlik, Petr [2 ,3 ]
机构：
[1] Leiden Univ, Math Inst, NL-2300 RA Leiden, Netherlands
[2] Univ West Bohemia, Fac Appl Sci, Dept Math, Univ 8, Plzen 30614, Czech Republic
[3] Univ West Bohemia, Fac Appl Sci, NTIS, Univ 8, Plzen 30614, Czech Republic
来源：
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS | 2019年 / 18卷 / 02期
关键词：
reaction-diffusion equation; lattice differential equation; travelling waves; nonlinear algebraic equations; CELLULAR NEURAL-NETWORKS; DISCRETE NAGUMO; PROPAGATION; DIFFUSION; SYSTEMS; MOTION; STABILITY; CRYSTAL; FAILURE; FRONTS;
D O I：
10.1137/18M1189221
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss bichromatic (two-color) front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatially heterogeneous 2-periodic equilibria and hence are not monotonic like the standard monochromatic fronts. We provide explicit criteria that can determine whether or not these fronts are stationary and show that the bichromatic fronts can travel in parameter regimes where the monochromatic fronts are pinned. The presence of these bichromatic waves allows the two stable homogeneous equilibria to spread out through the spatial domain towards each other, buffered by a shrinking intermediate zone in which the periodic pattern is visible.
引用
收藏
页码：973 / 1014
页数：42
相关论文
共 50 条
  • [31] Travelling Waves for Some Generalized Boussinesq Type Equations
    Popivanov, Petar
    [J]. INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES, INTEGRABILITY AND VECTOR FIELDS, 2011, 1340 : 126 - 133
  • [32] The impact of memristive coupling initial states on travelling waves in an ensemble of the FitzHugh-Nagumo oscillators
    Korneev, I. A.
    Semenov, V. V.
    Slepnev, A. V.
    Vadivasova, T. E.
    [J]. CHAOS SOLITONS & FRACTALS, 2021, 147
  • [33] Governing equations of envelopes created by nearly bichromatic waves on deep water
    Ben T. Nohara
    [J]. Nonlinear Dynamics, 2007, 50 : 49 - 60
  • [34] Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor
    A. B. Togueu Motcheyo
    G. J. Fezeu
    M. Siewe Siewe
    C. Nono Dueyou Buckjohn
    C. Tchawoua
    [J]. Journal of Computational Electronics, 2023, 22 : 41 - 49
  • [35] Travelling waves in discrete electrical lattice with nonlinear symmetric capacitor
    Motcheyo, A. B. Togueu
    Fezeu, G. J.
    Siewe, M. Siewe
    Buckjohn, C. Nono Dueyou
    Tchawoua, C.
    [J]. JOURNAL OF COMPUTATIONAL ELECTRONICS, 2023, 22 (01) : 41 - 49
  • [36] SMALL AMPLITUDE PERIODIC-WAVES FOR THE FITZHUGH-NAGUMO EQUATIONS
    SLEEMAN, BD
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1982, 14 (03) : 309 - 325
  • [37] Turning points and traveling waves in FitzHugh-Nagumo type equations
    Liu, WS
    Van Vleck, E
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 225 (02) : 381 - 410
  • [38] Algebraic traveling waves for some family of reaction-diffusion equations including the Nagumo equations
    Claudia Valls
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2017, 24
  • [39] Long waves associated with bichromatic waves
    Dong, GH
    Ye, WY
    Dodd, N
    [J]. CHINA OCEAN ENGINEERING, 2001, 15 (02) : 281 - 289
  • [40] Algebraic traveling waves for some family of reaction-diffusion equations including the Nagumo equations
    Valls, Claudia
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2017, 24 (03):
12345