A Predator-Prey Model with General Holling Interactions in Presence of Additional Food

Banshidhar Sahoo

doi:10.5923/j.plant.20120201.07

Abstract

A predator-prey model with general Holling type of interactions in presence of additional food is proposed. The stability of equilibrium points of the system is analysed. The bifurcation analysis is done with respect to Holling parameter as well as quantity of additional food. The model will be useful for construction of real food chain model for predicting future which will be important for bio-conservation and pest management.

Highlights

Understanding the relationship between predator and prey is a central goal in ecology
Many scholars have studied about continuous food chain models for several functional responses such as Holling-Tanner type[1,2], Beddington-DeAngelis type[3,4] and ratio dependent type[5,6]
There is no biological reason to prefer this special type of functional responses, but the exact predator functional response is more important

Summary

Introduction

Understanding the relationship between predator and prey is a central goal in ecology. There are many conceptual food chain models considering specific functional form of predator-prey interaction. Between very low and very high prey densities, the interaction function in most cases expected to be increasing [7]. If we consider constants ‘h1’ and ‘e1’ are as handling time of the predator per prey item and ability of the predator to detect the prey we have “A” and “B”, representing the food intake rate of predation and half saturation constant of the predator, to be 1/h1 and 1/h1e1, respectively[8]. If we assume that the constants ‘h2’and ‘e2’, respectively, represent the handling time of the predator per unit quantity of additional food and ability for the predator to detect the additional food, we have μ=e2/e1 and α=h2 /h1.

Dissipativeness

Stability Analysis

Numerical Results

Conclusions