ANZIAM  J.  48 (2006), 57-71
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
and
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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