Analyzing population dynamics models via Sumudu transform

TL;DR

This paper introduces a novel analytical approach combining Sumudu transform with variational iterative methods to solve complex population dynamics models, especially delay differential equations of pantograph type, revealing insights into population change patterns.

Contribution

It presents an innovative method for solving complex population models where traditional techniques are ineffective, expanding analytical tools in population dynamics.

Findings

Solutions for delay differential equations of pantograph type obtained.

Patterns and regularities in population changes identified.

Method applicable to chaotic population processes.

Abstract

This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. In this paper, population growth models are formulated in the form of delay differential equations of pantograph type which is a general form for the existing models. Innovative ways are presented for obtaining the solutions of population growth models where other analytic methods fail. Stimulating procedures for finding patterns and regularities in seemingly chaotic processes have been elucidated in this paper. How, when and why the changes in population sizes occur can be deduced through this study.