Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

Author:

Xia Wanjun1ORCID,Kundu Soumen2,Maitra Sarit2

Affiliation:

1. School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China

2. National Institute of Technology Durgapur, Durgapur, West Bengal 713209, India

Abstract

A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.

Funder

Provincial Foundation for Excellent Young Talents of Colleges and Universities of Anhui Province

Publisher

Hindawi Limited

Subject

Analysis

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