Bifurcation analysis of a host–parasitoid ecological model with the beddington-deangelis functional response

Tanuja Agrawal

doi:10.14419/gjma.v2i2.2405

Abstract

In this paper, a two species host-parasitoid model system is considered. The global dynamic behavior of the model is investigated through (local) stability results for its equilibriums and large time computer simulations. Many forms of complex dynamics such as chaos, periodic windows etc. are observed. The Hopf point and attractor crises exist for different set of parameter values. Keywords : Predator-Prey; Bifurcation; Chaos; Stability.

Highlights

Hosts and parasitoids are mostly univoltine and have no overlap between successive generations
P t is the parasitoid population size at generation t r is the intrinsic growth rate k is the carrying capacity of the environment a is the instantaneous search rate T is the total time initially available for the search Th is the handling time In the present work, we study Tang and Chen model [11] with Beddington –DeAngelis functional response which is an extension of the prey-dependent Holling's type II functional response
We have done the bifurcation analysis with respect to instantaneous search rate for different types of intraspecific competitions taking as parameter separately

Summary

Introduction

Hosts and parasitoids are mostly univoltine and have no overlap between successive generations Their interactions can be modeled by discrete differences [15,16,17,18]. Many researchers [5], [10] produced many discrete type host-parasitoid models with different ecological factors. P t is the parasitoid population size at generation t r is the intrinsic growth rate k is the carrying capacity of the environment a is the instantaneous search rate T is the total time initially available for the search Th is the handling time In the present work, we study Tang and Chen model [11] with Beddington –DeAngelis functional response which is an extension of the prey-dependent Holling's type II functional response. Where all the variables and parameters are the same as defined in (1.1)

Bifurcation analysis

Conclusion