ANZIAM J.
48 (2006), 5771

Travelling waves for the population genetics model with delay

Guojian Lin
Institute of Systems Science
Academy of Mathematics and Systems Science
Chinese Academy of Science
Beijing 100080
People's Republic of China
gjlin@amss.ac.cn



Rong Yuan
School of Mathematics
Beijing Normal University
Beijing
100875
People's Republic of China
ryuan@bnu.edu.cn



Abstract

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.

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