Publication Date

2025

Document Type

Dissertation/Thesis

First Advisor

Onyido, Maria Amarakristi

Second Advisor

Mancheva, Maya

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

Abstract

This thesis is based on the 2023 paper “Dynamics of Classical Solutions of a Two-Stage Structured Population Model with Nonlocal Dispersal.” We study the long-term behavior of a population with two life stages, juvenile and adult, moving across space using nonlocal dispersal mechanism. The main goal is to understand the conditions under which the species survives or goes extinct on the long run. This is determined by a key value called the principal spectrum point, λp.

First, using results from the literature on existence of solutions for general initial value problems on Banach spaces, we establish that for any given nonnegative initial function, the system has a unique, positive solution that exists for all time. Consequently, in studying the persistence and extinction dynamics, we found that when λp > 0, the population persists for all time, and in fact, if the birth and survival rates are positive, then every positive solution of the model is uniformly bounded away from zero. However, if λp ≤ 0 then the species goes into extinction. Finally, we present sufficient conditions based on the model parameters for determining the sign of the principal spectrum point.

Extent

57 pages

Language

en

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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