# American Institute of Mathematical Sciences

December  2014, 19(10): 3191-3207. doi: 10.3934/dcdsb.2014.19.3191

## A boundary value problem for integrodifference population models with cyclic kernels

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

Received  July 2013 Revised  December 2013 Published  October 2014

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.
Citation: Jon Jacobsen, Taylor McAdam. A boundary value problem for integrodifference population models with cyclic kernels. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3191-3207. doi: 10.3934/dcdsb.2014.19.3191
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