Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A boundary value problem for integrodifference population models with cyclic kernels

Pages: 3191 - 3207, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3191

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Jon Jacobsen - Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States (email)
Taylor McAdam - Department of Mathematics, University of Texas, Austin, TX 78712, United States (email)

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.

Keywords:  Integrodifference, population persistence, principal eigenvalue, cyclic kernels, trinomial coefficients.
Mathematics Subject Classification:  Primary: 45C05, 92B05; Secondary: 34B05.

Received: July 2013;      Revised: December 2013;      Available Online: October 2014.