A boundary value problem for integrodifference population models with cyclic kernels

Jon Jacobsen; Taylor McAdam

doi:10.3934/dcdsb.2014.19.3191

Article Contents

2014, Volume 19, Issue 10: 3191-3207. Doi: 10.3934/dcdsb.2014.19.3191

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A boundary value problem for integrodifference population models with cyclic kernels

Jon Jacobsen^1, and
Taylor McAdam^2,

1.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711
2.
Department of Mathematics, University of Texas, Austin, TX 78712

Received: June 30, 2013

Revised: November 30, 2013

Published: November 2014

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Abstract

The population dynamics of species with separate growth and dispersal stages can be modeled by a discrete-time, continuous-space integrodifference equation. Many authors have considered the case where the model parameters remain fixed over time, however real environments are constantly in flux. We develop a framework for analyzing the population dynamics when the dispersal parameters change over time in a cyclic fashion. In particular, for the case of $N$ cyclic dispersal kernels modeling movement in the presence of unidirectional flow, we derive a $2N^{th}$-order boundary value problem that can be used to study the linear stability of the associated integrodifference model.

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Mathematics Subject Classification: Primary: 45C05, 92B05; Secondary: 34B05.

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