广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (2): 66-72.doi: 10.16088/j.issn.1001-6600.2017.02.010

• • 上一篇    下一篇

一类带Lévy噪声的随机捕食-被捕食系统

黄开娇, 肖飞雁*   

  1. 广西师范大学数学与统计学院,广西桂林541004
  • 出版日期:2017-07-25 发布日期:2018-07-25
  • 通讯作者: 肖飞雁(1973—),女(土家族),湖南张家界人,广西师范大学副教授,博士。E-mail:fyxiao@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11301099,11461008);广西高等学校高水平创新团队及卓越学者计划

A Stochastic Predator-prey System with Lévy Jumps

HUANG Kaijiao, XIAO Feiyan*   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Online:2017-07-25 Published:2018-07-25

PDF (PC)

241

摘要： 本文建立了一类带Bedding-DeAngelis功能反应和Lévy噪声的随机捕食-被捕食系统,利用构建Lyapunov函数和停时技巧证明了该系统存在唯一的全局正解。在此基础上,通过构建函数证明这个解是随机最终有界的。最后,给出了物种趋于灭绝的充分条件。

关键词: Beddington-DeAngelis捕食模型, Lévy噪声, 灭绝性

Abstract: In this paper, a stochastic Bedding-DeAngelis predator-prey system with Lévy jumps is investigated. Using the construction of Lyapunov functions and stopping time technique, the existence of global unique positive solution is obtained. Based on that, by constructing some functions, it is shown that the solution of the system is stochastically ultimate bounded. Finally, some sufficient conditions of extinction are established.

Key words: Beddington-DeAngelis predator-prey model, Lévy jumps, extinction

中图分类号: 

  • O175
[1] HOLLING C S. Some characteristics of simple types of predation and parasitism[J]. The Canadian Entomologist, 1959,91(7): 385-398. DOI:10.4039/Ent91385-7.
[2] BEDDINGTON J R. Mutual interference between parasites or predators and its effect on searching efficiency[J]. Journal of Animal Ecology, 1975,44(1):331-340. DOI:10.2307/3866.
[3] HWANG T W. Global analysis of the predator-prey system with Beddington-DeAngelis functional response[J]. Journal of Mathematical Analysis and Applications, 2003, 281(1): 395-401. DOI:10.1016/S0022-247X(02)00395-5.
[4] XU Shenghu, L Weidong, LI Xiangfeng. Existence of global sulutions for a prey-predator model with Beddington-DeAngelis functional response and cross-diffusion[J]. Mathematica Applicata, 2009, 22(4):821-827.
[5] 汪洋. 具有Beddington-DeAngelis功能反应随机捕食者-食模型种群动力学分析[D]. 哈尔滨:哈尔滨工业大学, 2011.
[6] BAO Jianhai, MAO Xuerong, YIN G, et al. Competitive Lotka-Volterra population dynamics with jumps[J]. Nonlinear Analysis: Theory, Methods & Applications, 2011, 74(17): 6601-6616. DOI:10.1016/j.na.2011.06.043.
[7] BAO Jianhai, YUAN Chenggui. Stochastic population dynamics driven by Lévy noise[J]. Journal of Mathematical Analysis and Applications, 2012, 391(2): 363-375. DOI:10.1016/j.jmaa.2012.02.043.
[8] MAO Xuerong. Stochastic differential equations and their application[M]. Chichester: Horwood Publishing Limited, 1997:51-59.
[9] HWANG T W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response[J]. Journal of Mathematical Analysis and Applications, 2004, 290(1): 113-122. DOI:10.1016/j.jmaa.2003.09.073.
[10] MAO Xuerong, YUAN Chenggui, ZOU Jiezhong. Stochastic differential delay equations of population dynamics[J]. Journal of Mathematical Analysis and Applications, 2005, 304(1): 296-320. DOI:10.1016/j.jmaa.2004.09.027.
[11] 王克. 随机生物数学模型[M]. 北京:科学出版社, 2010.
[1] 李淑一, 韦煜明, 彭华勤. 含Ornstein-Uhlenbeck过程的随机SIS传染病模型[J]. 广西师范大学学报（自然科学版）, 2020, 38(4): 74-81.
[2] 李海燕, 韦煜明, 彭华勤. 具有双疾病的随机SIRS传染病模型的灭绝性与持久性分析[J]. 广西师范大学学报（自然科学版）, 2020, 38(2): 144-155.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发