IJPAM: Volume 37, No. 1 (2007)

PERIODICITY OF A ROSENZWEIG-MACARTHUR FOOD
CHAIN WITH IMPULSIVE RATIO-HARVESTING PREY

Guoping Pang$^1$Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi, 537000, P.R. CHINA, Fengyan Wang$^2$, Lansun Chen$^{3}$
$^1$Department of Mathematics and Computer Science
Yulin Normal University
Yulin, Guangxi, 537000, P.R. CHINA
e-mail: g.p.pang@163.com
$^2$College of Science
Jimei University
Xiamen, Fujian, 361021, P.R. CHINA
e-mail: wangfy68@163.com
$^{1,3}$Department of Applied Mathematics
Dalian University of Technology
Dalian, Liao Ning, 116024, P.R. CHINA
e-mail: lschen@amss.ac.cn


Abstract.In this paper, a Rosenzweig-MacArthur food chain with impulsive ratio-harvesting prey is investigated. By using Floquet theory and small amplitude perturbation skills, we discuss the boundary periodic solutions for predator-prey system under periodic pulsed conditions. The stability analysis of the boundary periodic solution yields an invasion threshold of the predator. Further, by use of the coincidence degree theorem and its related continuous theorem we prove the existence of the positive periodic solutions of the system when the value of the coefficient is large than the threshold.

Received: February 7, 2007

AMS Subject Classification: 34C25, 92D25

Key Words and Phrases: Rosenzweig-MacArthur food chain, impulsive effect, periodicity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 1