Hopf bifurcation analysis for a harvested differential-algebraic prey-predator model

Author

Liu, Wei ; Fu, Chaojin ; Zhang, Chunsheng

Author_Institution

Sch. of Math. & Comput. Sci., Xinyu Univ., Xinyu, China

fYear

2011

fDate

19-21 Oct. 2011

Firstpage

670

Lastpage

674

Abstract

In this paper, by means of Hopf bifurcation theory and the normal form method, Hopf bifurcation and local stability for a differential-algebraic predator-prey model with predator harvesting are considered. Our model is described by differential-algebraic equations due to economic factors are introduced into a traditional Lotka-Volterra predator-prey system. It shows that periodic solution occurs when the bifurcation parameter exceeds a certain limit. Some algebraic criteria on these issues are derived. Lastly, some numerical simulations are provided to support the effectiveness of our findings.

Keywords

Volterra equations; bifurcation; differential algebraic equations; nonlinear differential equations; predator-prey systems; stability; Hopf bifurcation analysis; Hopf bifurcation theory; Lotka-Volterra predator-prey system; algebraic criteria; bifurcation parameter; economic factors; harvested differential-algebraic prey-predator model; local stability; normal form method; predator harvesting; Bifurcation; Biological system modeling; Economics; Educational institutions; Mathematical model; Predator prey systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Advanced Computational Intelligence (IWACI), 2011 Fourth International Workshop on

Conference_Location

Wuhan

Print_ISBN

978-1-61284-374-2

Type

conf

DOI

10.1109/IWACI.2011.6160091

Filename

6160091