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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.

A boundary value problem for integrodifference population models with cyclic kernels