Reaction-diffusion waves in biology

被引：214
作者：
Volpert, V. [1 ]
Petrovskii, S. [2 ]
机构：
[1] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France
[2] Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England
来源：
PHYSICS OF LIFE REVIEWS | 2009年 / 6卷 / 04期
关键词：
Reaction-diffusion systems; Travelling waves; Population dynamics; Evolutionary branching; Cell dynamics; Leukemia; Atherosclerosis; PERIODIC TRAVELING-WAVES; PREDATOR-PREY SYSTEM; DYNAMICAL STABILIZATION; FRONT PROPAGATION; CALCIUM WAVES; INVASION; MODEL; COMPETITION; EQUATIONS; STABILITY;
D O I：
10.1016/j.plrev.2009.10.002
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The theory of reaction-diffusion waves begins in the 1930s with the works in population dynamics, combustion theory and chemical kinetics. At the present time, it is a well developed area of research which includes qualitative properties of travelling waves for the scalar reaction-diffusion equation and for system of equations, complex nonlinear dynamics, numerous applications in physics, chemistry, biology, medicine. This paper reviews biological applications of reaction-diffusion waves. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：267 / 310
页数：44
相关论文
共 138 条
  • [51] Adaptive dynamics:: modelling Darwin's divergence principle
    Genieys, Stphane
    Volpert, Vitaly
    Auger, Pierre
    [J]. COMPTES RENDUS BIOLOGIES, 2006, 329 (11) : 876 - 879
  • [52] Selection Theorem for Systems with Inheritance
    Gorban, A. N.
    [J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2007, 2 (04) : 1 - 45
  • [53] Travelling front solutions of a nonlocal Fisher equation
    Gourley, SA
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 2000, 41 (03) : 272 - 284
  • [54] TRAVELING FRONTS IN NONLINEAR DIFFUSION EQUATIONS
    HADELER, KP
    ROTHE, F
    [J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1975, 2 (03) : 251 - 263
  • [55] Stippling the Skin: Generation of Anatomical Periodicity by Reaction-Diffusion Mechanisms
    Headon, D. J.
    Painter, K. J.
    [J]. MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2009, 4 (04) : 83 - 102
  • [56] Singular limit of a spatially inhomogeneous Lotka-Volterra competition-diffusion system
    Hilhorst, D.
    Karali, G.
    Matano, H.
    Nakashima, K.
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (06) : 879 - 933
  • [57] A diffusive SI model with Allee effect and application to FIV
    Hilker, Frank M.
    Langlais, Michel
    Petrovskii, Sergei V.
    Malchow, Horst
    [J]. MATHEMATICAL BIOSCIENCES, 2007, 206 (01) : 61 - 80
  • [58] Hofbauer J., 1988, The Theory of Evolution and Dynamical Systems
  • [59] HORVATH J, 2009, SCIENCE 0508
  • [60] Morphogenesis of the branching reef coral Madracis mirabilis
    Kaandorp, JA
    Sloot, PMA
    Merks, RMH
    Bak, RPM
    Vermeij, MJA
    Maier, C
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2005, 272 (1559) : 127 - 133
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