On the reaction-diffusion replicator systems: spatial patterns and asymptotic behaviour

被引：9

作者：

Novozhilov, A. S. ^{[1
,2
]}

Posvyanskii, V. P. ^{[1
]}

Bratus, A. S. ^{[1
,2
]}

机构：

[1] Moscow State Univ Railway Engn, Moscow 127994, Russia

[2] Lomonosov Moscow State Univ, Moscow 119992, Russia

来源：

RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING | 2011年 / 26卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

TRAVELING-WAVES; HYPERCYCLES; STABILITY; PARASITES; DEPENDENCE; EVOLUTION; MODEL;

D O I：

10.1515/RJNAMM.2011.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The replicator equation is ubiquitous for many areas of mathematical biology. One of the major shortcomings of this equation is that it does not allow for an explicit spatial structure. Here we review analytical approaches to include spatial variables in the system. We also provide a concise exposition of results concerning the appearance of spatial patterns in replicator reaction diffusion systems.

引用

页码：555 / 564

页数：10

共 48 条

[41] Evolutionary dynamics in structured populations [J].

Nowak, Martin A. ;

Tarnita, Corina E. ;

Antal, Tibor .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2010, 365 (1537) :19-30

[42] EVOLUTIONARY GAMES FOR SPATIALLY DISPERSED POPULATIONS [J].

PRIOR, TG ;

HINES, WGS ;

CRESSMAN, R .

JOURNAL OF MATHEMATICAL BIOLOGY, 1993, 32 (01) :55-65

[43] REPLICATOR DYNAMICS [J].

SCHUSTER, P ;

SIGMUND, K .

JOURNAL OF THEORETICAL BIOLOGY, 1983, 100 (03) :533-538

[44] EVOLUTIONARILY STABLE STRATEGIES AND GAME DYNAMICS [J].

TAYLOR, PD ;

JONKER, LB .

MATHEMATICAL BIOSCIENCES, 1978, 40 (1-2) :145-156

[45] SPATIAL PATTERNS IN POPULATION CONFLICTS [J].

VICKERS, GT ;

HUTSON, VCL ;

BUDD, CJ .

JOURNAL OF MATHEMATICAL BIOLOGY, 1993, 31 (04) :411-430

[46] SPATIAL PATTERNS AND ESSS [J].

VICKERS, GT .

JOURNAL OF THEORETICAL BIOLOGY, 1989, 140 (01) :129-135

[47] SPATIAL PATTERNS AND TRAVELING WAVES IN POPULATION-GENETICS [J].

VICKERS, GT .

JOURNAL OF THEORETICAL BIOLOGY, 1991, 150 (03) :329-337

[48] SPATIAL STABILITY ANALYSIS OF EIGEN QUASISPECIES MODEL AND THE LESS THAN 5 MEMBERED HYPERCYCLE UNDER GLOBAL POPULATION REGULATION [J].

WEINBERGER, ED .

BULLETIN OF MATHEMATICAL BIOLOGY, 1991, 53 (04) :623-638

← 1 2 3 4 5 →