|Table of Contents|

Dynamic Behavior of Two-prey One-predator Impulsive System with Holling Ⅳ Functional Response

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2009年05期
Page:
619-625
Research Field:
Publishing date:

Info

Title:
Dynamic Behavior of Two-prey One-predator Impulsive System with Holling Ⅳ Functional Response
Author(s):
HUANG Wen-tao1WU Xing-jie2LI Wei2
1.School of Mathematics and Computational Science,Gulin University of Electronic Technology,Gulin 541004,China;2.Department of Mathematics,Hefei Teachers College,Hefei 230061,China
Keywords:
two-prey one-predator impulsive differential system impulsive comparison theorem bifurcation chaos Floquent theory
PACS:
O175.12
DOI:
-
Abstract:
Based on the strategy of integrated pest management,the dynamic behavior of a two-prey one-predator system with Holling Ⅳ functional response,impulsive ratio harvest and constant impulsive release is investigated.By using impulsive comparison theorem,Floquent theory and small amplitude perturbation skill,the critical value of impulsive release is given.One sufficient condition for the two preys to be extinct is proved,and the permanence of the system is proved.Moreover,the two sufficient conditions for the extinction of one of two preys and the permanence of remaining species are given.Numerical simulation shows that: with the increase of constant release,the system has more complex dynamics including periodic doubling bifurcation,chaos and periodic halving bifurcation.

References:

[ 1] BaninovD, Simeonov P. Impulsive differential equations: periodic solutions andapplications[M]. NewYork: Longman Scientific andTechnical Press, 1993. 26- 39.
[ 2] 陆征一, 周义仓. 数学生物学进展[M]. 北京:科学出版社, 2005. 131- 152.
[ 3] De BachP. BiologicalControl of Insect PestsandWeeds[M]. NewYork: Reinhold, 1964.
[ 4] VanLenternJC. IntegratedPestManagement inProtectedCrops[M]. London: ChapmanandHal,l 1995.
[ 5] LiuB, ZhangYJ, ChenLS. Thedynamical behaviorsof aLotka-Volterra predator-preymodel concerning integratedpest management[ J]. Nonlinear Analysis: RealWorldApplications, 2005(6): 227- 243.
[ 6] 刘兵,陈兰荪,张玉娟. 基于IPM策略的捕食与被捕食系统的动力学性质[ J]. 工程数学学报, 2005, 22( 1): 9- 14.
[ 7] PangGP, ChenLS. Analysisof aHollingÔ one-preda tor two-prey systemwithimpulsive effect[ J]. JournalofNanjing NormalUniversity, 2007, 33( 2): 1-5.
[ 8] WangXQ, WangWM, LinYZ, et a.l The dynamical complexity of an impulsiveWatt-type prey-predator system[ J]. Chaos, SolitonsandFractals, 2007( 8): 1-19.
[ 9] ZhangYJ, XiuZL, ChenLS. Dynamic complexity of a two-prey one-predator systemwith impulsiveeffect[ J]. Chaos, Solitons andFractals, 2005( 26): 131-139.

Memo

Memo:
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Last Update: 2012-11-19