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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