Population Dynamics with Infinite Leslie Matrices

TL;DR

This paper investigates solutions to discrete dynamical systems modeled by infinite Leslie matrices, using kneading matrices and determinants, applicable to population dynamics and self-reproducing systems.

Contribution

It introduces a method to determine solutions of infinite Leslie matrix models using kneading matrices and determinants, extending applicability beyond population models.

Findings

Provides a solution framework for infinite Leslie matrices

Applies to models of self-reproducing systems

Extends mathematical tools for infinite-dimensional systems

Abstract

Infinite Leslie matrices, introduced by Demetrius forty years ago are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but to models of self-reproducing machines and self-reproducing computer programs. The dynamics of theses systems can also be described in terms of infinite Leslie matrices.uation.