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Journal Articles The ANZIAM Journal Year : 2020

Evolutionary dynamics in discrete time for the perturbed positive definite replicator equation

Abstract

The population dynamics for the replicator equation are 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.
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Dates and versions

hal-02892186 , version 1 (07-07-2020)

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  • HAL Id : hal-02892186 , version 1

Cite

Amie Albrecht, Konstantin Avrachenkov, Phil Howlett, Geetika Verma. Evolutionary dynamics in discrete time for the perturbed positive definite replicator equation. The ANZIAM Journal, 2020, 62 (2), pp.148-184. ⟨hal-02892186⟩
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