IJPAM: Volume 48, No. 2 (2008)

A STAGE-STRUCTURED PREDATOR-PREY SYSTEM WITH
TIME DELAY AND HOLLING TYPE-III
FUNCTIONAL RESPONSE

Lingshu Wang$^1$School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, P.R. CHINA, Rui Xu$^2$, Guanghui Feng$^3$
$^{1,2,3}$Institute of Applied Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang, 050003, P.R. CHINA
$^1$e-mail: wanglingshu@126.com
$^2$e-mail: rxu88@yahoo.com.cn
$^1$School of Mathematics and Statistics
Hebei University of Economics and Business
Shijiazhuang, 050061, P.R. CHINA


Abstract.A stage-structured predator-prey system with time delay and Holling type-III functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

Received: June 20, 2008

AMS Subject Classification: 34K15, 92D25

Key Words and Phrases: predator-prey system, stage structure, time delay, Holling type-III functional response, stability, Hopf bifurcation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2