Continuous and impulsive harvesting strategies in a stage-structured predator–prey model with time delay

Pei Yongzhen, Li Changguo and Chen Lansun

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 79, issue 10, 2994-3008

Abstract: In this paper, the continuous and impulsive harvesting policies are considered in a predator–prey system with stage-structure. In the case in which a continuous harvesting is used, it is shown that the mature predator becomes extinct under appropriate conditions. In the case in which an impulsive harvesting is used, using the discrete dynamical system determined by the stroboscopic map, we obtain the mature predator-eradication periodic solution of the system which is globally attractive. The conditions of permanence are established by the method of comparison involving multiple Liapunov functions and auxiliary function. These results indicate that: a short period of pulse harvest is a sufficient condition for the eradication of the population; the impulsive harvest policy is more effective than the continuous one from eradicating predator point of view. Our results offer a more economical and safe strategy in controlling pest in contrast with biological control and chemical control. Furthermore, we give a summary of the dynamic behavior when the impulsive period takes values in different intervals. Finally, numerical results show that the impulsive system we considered has more complex dynamics including quasi-periodic oscillation and chaos.

Keywords: Time delay; Stage-structure; Harvest; Extinction; Permanence (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037847540900007X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2009:i:10:p:2994-3008

DOI: 10.1016/j.matcom.2009.01.003

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().