聂文静,王辉,胡志兴,廖福成

• 1:北京科技大学数理学院

摘要(Abstract)：

将环境中的白噪声和Beddington-De Angelis型功能反应函数考虑到含有修改的Leslie-Cower类型种群系统中,得到一类具有修改的Leslie-Cower类型的随机三物种捕食-被捕食模型.首先利用随机微分方程比较原理得到具有修改的Leslie-Cower类型的随机三物种捕食-被捕食模型,在任意给定的正的初值条件下,系统存在唯一的全局正解;然后,利用随机微分方程比较原理和微分中值定理得到,在一定条件下三物种是随机强平均持久,而且当白噪声超出某个范围时会使三个物种都趋于灭亡.

关键词(KeyWords)： Leslie-Cower型功能;Beddington-De Angelis型功能;随机比较方程;高斯白噪声

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金资助项目(11471034,61174209);; 北京科技大学冶金工程研究院基础研究基金项目(YJ2012-001)

作者(Author): 聂文静,王辉,胡志兴,廖福成

DOI: 10.13705/j.issn.1671-6841.2016035

参考文献(References)：

• [1]UPADHYAY R K,NAJI R K.Dynamics of a three species food chain model with Crowley-Martin type functional response[J].Chaos,solitons&fractals,2009,42(3):1337-1346.
• [2]SHI X Y,ZOU X Y,SONG X Y.Analysis of a stage-structured predator-prey model with Crowley-Martin function[J].Applied mathematics and computation,2011,36(1):459-472.
• [3]MENG X Y,HUO H F,XIANG H,et al.Stability in a predator-prey model with Crowley-Martin function and stage structure for prey[J].Applied mathematics and computation,2014,232(3):810-819.
• [4]LI H X.Asymptotic behavior and multiplicity for a diffusive Leslie-Gower predator-prey system with Crowley-Martin functional response[J].Applied mathematics and computation,2014,68(7):693-705.
• [5]LIU M,WANG K.Stochastic Lotka-Volterra systems with Lévy noise[J].Jourmal of mathematical analysis and application,2014,410(2):750-763.
• [6]LIU M,BAI C Z.Global asymptotic stability of a stochastic delayed predator-prey model with Beddington-De Angelis functional response[J].Applied mathematics and computation,2014,226(1):581-588.
• [7]KUNAL C,KUNAL D,YU H G.Modeling and analysis of a modified leslie-Gower type three species food chain model with an impulsive control strategy[J].Nonlinear analysis:hybrid systems,2015,(15):171-184.
• [8]AZIZ-ALAOUI M A.Study of Leslie-Gower-type tritrophic population model[J].Chaos solitons fractals 2002,14(8):1275-1293.
• [9]HALDARS,CHAKRABORTYK,DAS K.Bifurcation and control of an eco-epidemiolnical system with environmental fluctuations:a stochastic approach[J].Nonlinear dynamics,2015,80(3):1187-1207.
• [10]QIU H,LIU M,WANG K,et al.Dynamics of a stochastic predator prey system with Beddington-De Angelis functional response[J].Mathematics and computation,2012,219(4):2303-2312.
• [11]LIU X Q,ZHONG S M,TIAN B D.Asymptotic properties of a stochastic predator prey model with Crowley-Martin functional response[J].Applied mathematics and computation,2013,43(1/2):479-490.
• [12]OKSENDAL B.Stochastic Differential Equations and Applications[M].Horwood Publishing:Avadem,c Press,1997.
• [13]JI C Y,JIANG D Q,SHI N Z.Analysis of a predator-prey model with Modified Leslie-Gower and Holling-type II schemes with stochastic perturbation[J].Mathematical analysis and applications,2009,359(2):482-498.
• [14]MAO X R,SOTIRIES S,ERIC R.Asymptotic behavior of stochastic Lotka-Volterra,model[J].Mathematical analysis and applications.2003,287(1):141-156.
• [15]HIGHAM D.An algorithmic introduction to numerical simulation of stochastic differential equations[J].SIAM review.2001,43(3):525-546.