[1]章培军,王震,杨颖惠.具有收获和Beddington-DeAngelis功能反应的捕食-食饵模型[J].华侨大学学报(自然科学版),2017,38(4):579-584.[doi:10.11830/ISSN.1000-5013.201704025]
　ZHANG Peijun,WANG Zhen,YANG Yinghui.Predator-Prey Model With Beddington-DeAngelis Functional Response and Harvesting[J].Journal of Huaqiao University(Natural Science),2017,38(4):579-584.[doi:10.11830/ISSN.1000-5013.201704025]
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具有收获和Beddington-DeAngelis功能反应的捕食-食饵模型()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第38卷
期数:
2017年第4期
页码:
579-584
栏目:
出版日期:
2017-07-10

文章信息/Info

Title:
Predator-Prey Model With Beddington-DeAngelis Functional Response and Harvesting
文章编号:
1000-5013(2017)04-0579-06
作者:
章培军1; 2;  王震1; 2;  杨颖惠3
1. 西京学院 理学院, 陕西 西安 710123;2. 西京学院 智能控制技术研发中心, 陕西 西安 710123;3. 西南交通大学 数学学院, 四川 成都 611756
Author(s):
ZHANG Peijun1; 2;  WANG Zhen1; 2;  YANG Yinghui3
1. School of Science, Xijing University, Xi’an 710123, China; 2.Intelligent Control Technology Research and Development Center, Xijing University, Xi’an 710123, China; 3. School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China
关键词:
Beddington-DeAngelis功能反应;  捕食-食饵模型;  时滞;  阶段结构;  Hopf分支
Keywords:
Beddington-deAngelis functional response;  predator-prey model;  time delay;  stage structure;  Hopf bifurcation
分类号:
O175;Q141
DOI:
10.11830/ISSN.1000-5013.201704025
文献标志码:
A
摘要:
研究食饵具有阶段结构,捕食者具有收获和时滞的Beddington-DeAngelis功能反应的捕食-食饵模型.选取合适的收获率,通过分析相应平衡点处的特征方程,得到各平衡点局部渐近稳定的条件.以时滞τ为分支参数,运用Hopf分支理论,得到当τ经过临界值τ0时系统出现Hopf分支.最后,用Matlab软件进行数值仿真,并验证结论的正确性.
Abstract:
A predator-prey model with Beddington-DeAngelis functional response of predator with harvesting and time delay and the stage structure for prey are investigated in this paper. Select the appropriate harvest rate, the conditions for the local asymptotic stability of the equilibrium point are obtained by analyzing the characteristic equation of the corresponding equilibrium point; by means of the Hopf bifurcation theorem and considering the delay τ as a bifurcation parameter, Hopf bifurcation occurs when τ passes through the critical value τ0. Finally, Matlab is employed to carry out numerical simulation to verify our results.

参考文献/References:

[1] HOLLING C S.The functional response of predator to prey density and its role in mimicry and population regulation[J].Memoirs of the Entomological Society of Canada,1965,97(45):1-60.
[2] JOST C,ELLNER S P.Testing for predator dependence in predator-prey dynamics: A non-parametric approach[J].Proceedings of the Royal Society B Biological Sciences,2000,267(1453):1611-1620.
[3] HASSELL M P,VARLEY C C.New inductive population model for insect parasites and its bearing on biological control[J].Nature,1969,223(5211):1133-1137.
[4] CROWLEY P H,MARTIN E K.Functional response and interference within and between year classes of a dragonfly population[J].Journal of the North American Benthological Society,1989,8(3):211-221.
[5] BEDDINGTON J R.Mutual interference between parasites or predators and its effect on searching efficiency[J].Journal of Animal Ecology,1975,44(1):331-40.
[6] DEANGELIS D L,GOLDSTEIN R A,O’NEILL R V.A model for tropic interaction[J].Ecology,1975,56(4):881-892.
[7] CHEN Fengde,CHEN Yuming,SHI Jinlin.Stability of the boundary solution of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response[J].Journal of Mathematical Analysis and Applications,2008,344(2):1057-1067.
[8] LIU Meng,WANG Ke.Global stability of stage-structured predator-prey models with Beddington-DeAngelis functional response[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(9):3792-3797.
[9] PALLAV P J,MANDAL P K,LAHIRI K K.A delayed ratio-dependent predator-prey model of interacting populations with Holling type Ⅲ functional response[J].Nonlinear Dynamics,2014,76(1):201-220.
[10] CELIKÇ.Stability and Hopf Bifurcation in a delayed ratio dependent Holling-Tanner type model[J].Applied Mathematics and Computation,2015,255:228-237.
[11] WANG Xuedi,PENG Miao,LIU Xiuyu.Stability and Hopf bifurcation analysis of aratio-dependent predator-prey model with two time delays and Holling type Ⅲ functional response[J].Applied Mathematics and Computation,2015,268:496-508.
[12] XIA Yonghui,CAO Jinde,CHENG Suisun.Multiple periodic solutions of a delayed stage-structured predator-prey model with non-monotone functional responses[J].Applied Mathematical Modelling,2007,31(9):1947-1959.
[13] CHAKRABORTY K,JANA S,KAR T K.Global dynamics and bifurcation in a stage structured prey-predator fishery model with harvesting[J].Applied Mathematics and Computation,2012,218(18):9271-9290.
[14] ALOMARI J F M.The effect of state dependent delay and harvesting on a stage-structured predator-prey model[J].Applied Mathematics and Computation,2015,271(C):142-153.
[15] LIU Chao,ZHANG Qingling,LI Jinna,et al.Stability analysis in a delayed prey-predator-resource model with harvest effort and stage structure[J].Applied Mathematics and Computation,2014,238(5):177-192.
[16] BOONRANGSIMAN S,BUNWONG K,MOORE E J,et al.A bifurcation path to chaos in a time-delay fisheries predator-prey model with prey consumption by immature and mature predators[J].Mathematics and Computers in Simulation,2016,124:16-29.
[17] KUANG Yang.Delay differential equations with applications in population dynamics[M].New York:Academic Press,1993:24-25.
[18] XU Rui.Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response[J].Nonlinear Dyn,2012,67(2):1683-1693.
[19] SONG Yongli,HAN Maoan,WEI Junjie.Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays[J].Physica D,2005,200(3/4):185-204.
[20] HANSARD B D,KAZARINOFF N D,WAN Y H.Theory and applications of Hopf bifurcation[M].Cambridge:Cambridge University Press,1981:1-132.

备注/Memo

备注/Memo:
收稿日期: 2017-01-11
通信作者: 章培军(1984-),男,讲师,主要从事生物数学与计算机模拟、常微分方程与动力系统的研究.E-mail:zhangpj2006@126.com.
基金项目: 国家自然科学基金资助项目(61473237); 陕西省自然科学基础研究计划资助项目(2016JM1024); 陕西省教育厅科研计划项目(15JK2181); 西京学院科研基金资助项目(XJ160143)
更新日期/Last Update: 2017-07-20