Date of Award
5-7-2026
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
William Barker
Abstract
We investigate the spatial dynamics of a population modeled by a general discrete integrodifference equation incorporating k-generation long-term memory. While classical models rely solely on the im- mediately preceding state to determine population growth and dispersal, introducing multiple past states causes the associated evolution operator to lose compactness. Consequently, standard fixed- point theorems are insufficient to prove the existence of traveling wave solutions. We overcome this difficulty by constructing a time-independent moving frame operator and employing the monotone iteration method. By assuming the fecundity function is locally Lipschitz, bounded, and nondecreasing on a specified interval, and by relaxing continuity requirements on the dispersal kernel, we establish the existence of monotone traveling wave fronts connecting the trivial state to the carrying capacity. We also use Lebesgue’s dominated convergence theorem together with Dini’s theorem to obtain uniform convergence on compact sets and continuity of the resulting wave profile.
Recommended Citation
Sanders, Austin Kernel, "Monotone Traveling Waves in a General Discrete Model for Populations with K-Generation Long-Term Memory" (2026). Theses and Dissertations. 1333.
https://research.ualr.edu/etd/1333
