Monotone traveling waves in a general discrete model for populations with long term memory

William Barker; Ahlam  Alzahrani

doi:10.26637/mjm11S/008

Abstract

In this paper we consider the existence of monotone traveling waves for a class of general integral difference models for populations that are dependent on the previous state term and also on long term memory. This allows us to consider multiple past states. For this model we will have to deal with the non-compactness of the evolution operator when we prove the existence of a fixed point. This difficulty will be overcome by using the Monotone Iteration Method and Dini’s Theorem to show uniform convergence of an iterative evolution operator to a continuous wave function.

Keywords:

Traveling waves, spreading speed, delay effect, partially sedentary population

Mathematics Subject Classification:

92D25, 37N25, 39A22

Authors Imprint References Funding Related Articles Downloads

William Barker Department of Mathematics,University of Arkansas at Little Rock, Little Rock, Arkansas, USA. https://orcid.org/0000-0001-5663-4967
Ahlam Alzahrani Department of Mathematics,University of Arkansas at Little Rock, Little Rock, Arkansas, USA. https://orcid.org/0009-0008-3452-8256

Pages: 115-124
Date Published: 01-10-2023
Vol. 11 No. S (2023): Malaya Journal of Matematik (MJM): Special Issue Dedicated to Professor Gaston M. N'Guérékata’s 70th Birthday

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