Modeling and Analysis of Prey Predator Systems in Population Biology

Abstract

Mathematical biology is a rapidly growing and widely recognized field that is one of the newlinemost intriguing applications of mathematics in the modern age. Mathematics and biology are newlinecombined in the fields of population dynamics and epidemiology. The study of population newlinebiology is concerned with the interaction between biological populations and their environment. newlineThis thesis examines prey-predator models qualitatively through differential equations, newlinewith the objective of improving our understanding of complex ecological dynamics. This research newlineanalyzes the stability of these models, their bifurcation and their formation of patterns using a newlinevariety of mathematical and computational techniques. newlineAn introduction to mathematical biology is presented initially, along with an explanation newlineof the thesis objectives and motivation. These topics include population dynamics, preypredator newlineequations, functional responses and non-autonomous systems. The detailed analyses newlinethat follow are based on a variety of different models, including delay, diffusive and epidemic newlinemodels. newlineThe research then explores the dynamics of two prey species and one predator species newlineby incorporating an additive Allee effect and a Holling type II functional response. A nondimensionalized newlinemodel is used to analyze population stability and the impact of real-world newlineissues like climate change and biodiversity loss on species interactions. We extend the model newlinefrom an ODE to a PDE system to account for spatial diffusion, enabling a deeper understanding newlineof spatial dependencies newline