|Table of Contents|

Stability of a stochastic predator-prey system with prey refuge(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2017年02期
Page:
214-219
Research Field:
Publishing date:

Info

Title:
Stability of a stochastic predator-prey system with prey refuge
Author(s):
 LIU ZhiyiZHENG WeiweiZHU Xiaolu
 School of Science, Xi’an Polytechnic University, Xi’an 710048, China
Keywords:
stochastic perturbation Itô formula stochastically ultimately bounded global stochastically asymptotic stability
PACS:
O 29; O 211.63
DOI:
10.13338/j.issn.1006-8341.2017.02.009
Abstract:
The stochastic predator-prey system incorporating a prey refuge and Holling Ⅱ functional response is investigated. Using Itô formula and Lyapunov function to show that there is a unique global positive solution to the stochastic system. And the positive solution to the stochastic system is stochastically ultimately bounded by using Chebyshev inequality. The sufficient conditions of global stochastically asymptotic stability of the positive solution to the stochastic system is derived through the stochastically stability theory.

References:

[1] TAPAN Kumar Kar.Stability analysis of a prey-predator model incorporating a prey refuge[J].Communications in Nonlinear Science and Numerical Simulation,2005,10(6):681-691. [2] 赵磊,郑唯唯.具Holling IV 功能反应和避难所的捕食系统的定性分析[J].西安工程大学学报,2012,26(6):807-810. ZHAO Lei,ZHENG Weiwei.Qualitative analysis of a predator-prey model with Holling IV functional incorporating a constant refuge[J].Journal of Xi’an Polytechnic University,2012,26(6):807-810. [3] WANG Huicheng,XIA Yonghui,ZOU Changwu.Periodic solution of a nonautonomous predator-prey model with a constant refuge[J].Journal of Shanghai Normal University(Natural Sciences),2015,44(3):314-321. [4] 陈柳娟,陈凤德.食饵具庇护所的基于比率捕食-食饵模型的全局稳定性和分支[J].数学学报中文版,2014,57(2):301-310. CHEN Liujuan,CHEN Fengde.Global stability and bifurcation of a Ratio-dependent predator-prey model with prey refuge[J].Acta Mathematica Sinica(Chinese Series),2014,57(2):301-310. [5] 宋爱丽,阿吉木·优力达西.具有时滞和避难所的捕食者-两共存食饵模型[J].生物数学学报,2012,27(2):290-296. SONG Aili,AJIM·Yoldax.A one predator-two cooperative prey model with delays and refuges[J].Journal of Biomathematics,2012,27(2):290-296. [6] 陈新一.一类具有时滞和避难所的捕食者-两共存食饵模型[J].生物数学学报,2015,30(3):436-442. CHEN Xinyi.A predator-two cooperative prey model with delays and refuges[J].Journal of Biomathematics,2015,30(3):436-442. [7] LYU Jingliang,WANG Ke.Asymptotic properties of a stochastic predator-prey system with Holling II functional response[J].Commun Nonlinear Sci Numer Simulat,2011,16(10):4037-4048. [8] LIU Meng,WANG Ke.Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response[J].Commun Nonlinear Sci Numer Simulat,2011,16(3):1114-1121. [9] LIU Xianqing,ZHONG Shouming,TIAN Baodan,et al.Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response[J].J Appl Math Comput,2013,43:479-490. [10] 孟笑莹,邓飞其,彭云建.具有随机扰动的食饵-捕食系统的稳定性[J].系统与工程电子技术,2011,33(2):385-389. MENG Xiaoying,DENG Feiqi,PENG Yunjian.Stability of a prey-predator system with perturbation[J].Systems Engineering Electronics,2011,33(2):385-389. [11] LIU Meng,WANG Ke.Global stability of stage-structured predator-prey models with B-D functional response[J].Commun Nonlinear Sci Numer Simulat,2011,16(9):3792-3797. [12] 聂文静,王辉,胡志兴,等.一类具有随机项的三物种捕食-被捕食模型[J].郑州大学学报(理学版),2016,48(3):1-9. NIE Wenjing,WANG Hui,HU Zhixing,et al.A delayed three species food chain predator-prey model with stochastic perturbation[J].Journal of Zhengzhou University(Natural Science Edition),2016,48(3):1-9. [13] LIU Meng,WANG Ke.Persistence,extinction and global asymptotical stability of a non-autonomous predator-prey model with random perturbation[J].Applied Mathematical Modelling,2012,36(11):5344-5353. [14] LIU Meng,WANG Ke.Dynamics of a non-autonomous stochastic Gilpin-Ayala model[J].J Appl Math Comput,2013,43(1/2):351-368. [15] LI Dan,CUI Jingan,SONG Guohua.Permanence and extinction for a single-species system with jump-diffusion[J].Journal of Mathematical Analysis and Applications,2015,430(1):438-464. [16] 臧彦超,李俊平.带Beddington-DeAngelis功能反应和Lévy噪声的随机捕食-被捕食系统的渐近性质[J].应用数学学报,2015,38(2):340-349. ZANG Yanchao,LI Junping.A dynamics of a stochastic predator-prey system with Beddington-DeAngelis functional response and Lévy jumps[J].Acta Mathematicae Applicatae Sinica,2015,38(2):340-349.

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Last Update: 2017-07-22