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Travelling waves for the population genetics model with delay

Published online by Cambridge University Press:  17 February 2009

Guojian Lin  and
Rong Yuan
Guojian Lin
Affiliation:
Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, People's Republic of China; e-mail: gjlin@amss.ac.cn.
Rong Yuan
Affiliation:
School of Mathematics, Beijing Normal University, Beijing, 100875, People's Republic of China; e-mail: ryuan@bnu.edu.cn.
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Abstract

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Under the assumptions that the spatial variable is one dimensional and the distributed delay kernel is the general Gamma distributed delay kernel, when the average delay is small, the existence of travelling wave solutions for the population genetics model with distributed delay is obtained by using the linear chain trick and geometric singular perturbation theory. On the other hand, for the population genetics model with small discrete delay, the existence of travelling wave solutions is obtained by employing a technique which is based on a result concerning the existence of the inertial manifold for small discrete delay equations.

Keywords

travelling wavepopulation genetics modelgeometric singular perturbation theoryinertial manifold.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 57 - 71
Copyright
Copyright © Australian Mathematical Society 2006

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