A Study On Predator- Prey Systems With Immigrant Prey With And Without Harvesting

ABSTRACT

The study of predator prey model with immigrant prey with and without harvesting has received great attention from both theoretical and mathematical biologists and has been studied intensively and extensively. Different literatures on interaction between species have been surveyed.

In this document we establish sufficient stability criteria, criteria for the existence of periodic solution and Hopf bifurcations of a predator prey systems with immigrant prey without and with harvesting of predator. The ecological system in nature can be balanced by introducing an immigrant prey to ensure existence of both preys and predators. Harvesting of predator also can be used as a stabilizing factor as far as they depend on prey for their survival.

The approach involves the use of software program (mat lab) in analyzing Equilibrium points, periodic solutions, Hopf bifurcations and its related theorems.

This thesis has four chapters organized as follows

Chapter 1: General Introduction, literature review, study objectives, significant of the

Study, application, and limitation of the study

Chapter 2: Definition and methodology of predator prey systems with immigrant prey,

with and without harvesting of predator.

Chapter 3: Predator prey systems with immigrant prey without harvesting

Chapter 4: Predator prey systems with immigrant prey with predators harvesting

at a constant rate and at a rate proportional to predator population