EVOLUTIONARY DYNAMICS IN DISCRETE TIME FOR THE PERTURBED POSITIVE DEFINITE REPLICATOR EQUATION

被引：3

作者：

Albrecht, Amie ^{[1
]}

Avrachenkov, Konstantin ^{[2
]}

Howlett, Phil ^{[1
]}

Verma, Geetika ^{[1
]}

机构：

[1] Univ South Australia, CIAM, SCG, Toki, Gifu 5095292, Japan

[2] INRIA, COSTNET CA15109, Le Chesnay, France

来源：

ANZIAM JOURNAL | 2020年 / 62卷 / 02期

关键词：

replicator equation; discrete time; random perturbations; BEHAVIOR;

D O I：

10.1017/S1446181120000140

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.

引用

页码：148 / 184

页数：37

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