On the Stability of Delay Population Dynamics Related with Allee Effects

O A Gumus,H Kose

doi:10.3390/mca17010056

Abstract

In recent years, many scientists have focus on the studies of the Allee effect in population dynamics. This paper presents the stability analysis of equilibrium points of population dynamics with Allee effect which occurs at low population density.

Highlights

INTRODUCTIONWhen previous studies have been examined on population dynamics including differential and difference equations, it is generally observed that Allee effect can have either a stable or an unstable effect on the system [1,3,5,6,8,9,11-14,16-19]
When previous studies have been examined on population dynamics including differential and difference equations, it is generally observed that Allee effect can have either a stable or an unstable effect on the system [1,3,5,6,8,9,11-14,16-19].discrete-time models are more suitable for numerical solutions and calculations [10,15].Allee effect was first defined by Allee as negative density dependence when the growth rate of the population decreases in low population density
Former studies indicate that Allee effect has different effects on different populations

Summary

INTRODUCTION

When previous studies have been examined on population dynamics including differential and difference equations, it is generally observed that Allee effect can have either a stable or an unstable effect on the system [1,3,5,6,8,9,11-14,16-19]. Stability analysis is an important research topic in such studies In this present study, our purpose is to investigate and compare the stability of equilibrium point with and without Allee effect by considering a more general state of the model studied in [3]. This paper is organized as follows: In section 2, first of all, we give a characterization of the stability of the equilibrium points of Eq(1). We study the local stability analysis of the equilibrium points of Eq(1) with the addition of Allee effect at time t 2, t and (t,t 2). We consider the following non-linear delay difference equation by the addition of Allee effect to discrete delay model Eq(1).

Allee effect at time t-1

Allee effect at time t

CONCLUSION