Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

被引:17
作者
Cheng, Huidong [1 ]
Wang, Fang [1 ]
Zhang, Tongqian [1 ]
机构
[1] Shandong Univ Sci & Technol, Coll Sci, Qingdao 266510, Peoples R China
基金
中国国家自然科学基金;
关键词
PEST-MANAGEMENT; TIME-DELAY; STRATEGIES; SYSTEM;
D O I
10.1155/2012/181752
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.
引用
收藏
页数:21
相关论文
共 14 条
[1]   Permanence of population growth models with impulsive effects [J].
Ballinger, G ;
Liu, X .
MATHEMATICAL AND COMPUTER MODELLING, 1997, 26 (12) :59-72
[2]  
Holling C. S., 1965, Mem ent Soc Canada Ottawa, Vno. 45, P1
[3]  
Jiang GR, 2005, MATH BIOSCI ENG, V2, P329
[4]   Impulsive state feedback control of a predator-prey model [J].
Jiang, Guirong ;
Lu, Qishao .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 200 (01) :193-207
[5]   GLOBAL ATTRACTIVITY OF A STAGE-STRUCTURE VARIABLE COEFFICIENTS PREDATOR-PREY SYSTEM WITH TIME DELAY AND IMPULSIVE PERTURBATIONS ON PREDATORS [J].
Jiao, Jianjun ;
Chen, Lansun .
INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2008, 1 (02) :197-208
[6]   Dynamic complexities of a Holling I predator-prey model concerning periodic biological and chemical control [J].
Liu, B ;
Zhang, YJ ;
Chen, LS .
CHAOS SOLITONS & FRACTALS, 2004, 22 (01) :123-134
[7]   A stage-structured SI eco-epidemiological model with time delay and impulsive controlling [J].
Meng, Xinzhu ;
Chen, Lansun .
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2008, 21 (03) :427-440
[8]   Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects [J].
Nie, Linfei ;
Peng, Jigen ;
Teng, Zhidong ;
Hu, Lin .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 224 (02) :544-555
[9]   A stage-structured predator-prey model with disturbing pulse and time delays [J].
Song, Xinyu ;
Hao, Meiying ;
Meng, Xinzhu .
APPLIED MATHEMATICAL MODELLING, 2009, 33 (01) :211-223
[10]   Modelling and optimization of a continuous stirred tank reactor with feedback control and pulse feeding [J].
Sun, Kaibiao ;
Kasperski, Andrzej ;
Tian, Yuan ;
Chen, Lansun .
CHEMICAL ENGINEERING AND PROCESSING-PROCESS INTENSIFICATION, 2011, 50 (07) :675-686