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IMA Journal of Applied Mathematics 2003 68(4):409-439; doi:10.1093/imamat/68.4.409
© 2003 by Institute of Mathematics and its Applications
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Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction

Peixuan Weng1, Huaxiong Huang2 and Jianhong Wu2

1 Department of Mathematics, South China Normal University, Guangzhou 510631, People's Republic of China 2 Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3

In this paper, we derive a lattice model for a single species in a one-dimensional patchy environment with infinite number of patches connected locally by diffusion. Under the assumption that the death and diffusion rates of the mature population are age independent, we show that the dynamics of the mature population is governed by a lattice delay differential equation with global interactions. We study the well-posedness of the initial-value problem and obtain the existence of monotone travelling waves for wave speeds c > c*. We show that the minimal wave speed c* is also the asymptotic speed of propagation, which depends on the maturation period and the diffusion rate of mature population monotonically.

Keywords: lattice equation; age structure; delay; travelling wave; monotone iteration; asymptotic speed of propagation; global interaction.

Received 12 April 2002.


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