IJPAM: Volume 55, No. 4 (2009)

A DELAYED RATIO-DEPENDENT PREDATOR-PREY
SYSTEM WITH STAGE-STRUCTURED AND
IMPULSIVE STOCKING ON PREDATOR

Zuxiong Li$^1$, Lansun Chen$^2$
$^{1,2}$Department of Applied Mathematics
Dalian University of Technology
Dalian, 116024, P.R. CHINA
$^1$e-mail: lizx0427@126.com
$^2$e-mail: lschen@amss.ac.cn


Abstract.In this paper, a delayed ratio-dependent Holling-III predator-prey system with stage-structured and impulsive stocking on predator and continuous harvesting on prey is considered. We obtain sufficient conditions of the global attractivity of prey-extinction periodic solution and the permanence of the system. These results show that the behavior of impulsive stocking on predator plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results show that the biological resource management is effective and reliable.

Received: August 7, 2009

AMS Subject Classification: 34A37, 34K45

Key Words and Phrases: stage-structured, ratio-dependent, impulsive effect, globally attractivity, permanence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 4