带一般Lévy跳和白噪声干扰的随机三种群食物链模型的生存性分析

doi:10.3969/j.issn.0253-2778.2018.08.004

中国科学技术大学学报 ›› 2018, Vol. 48 ›› Issue (8): 622-630.DOI: 10.3969/j.issn.0253-2778.2018.08.004

带一般Lévy跳和白噪声干扰的随机三种群食物链模型的生存性分析

曾婷，滕志东

新疆大学数学与系统科学学院,新疆乌鲁木齐 830046

收稿日期:2017-06-05 修回日期:2017-07-18 接受日期:2017-07-18 出版日期:2018-08-31 发布日期:2017-07-18
通讯作者: 滕志东
作者简介:曾婷,女,1992年生，硕士生.研究方向: 常微分方程及其应用.E-mail: misunderzeng@163.com
基金资助:
新疆维吾尔自治区重点实验室开放课题（2016D03022）资助.

Survival analysis of stochastic three-species food chain model with white noise and general Lévy jumps

ZENG Ting, TENG Zhidong

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China

Received:2017-06-05 Revised:2017-07-18 Accepted:2017-07-18 Online:2018-08-31 Published:2017-07-18

摘要/Abstract

摘要： 对一类一般Lévy跳和白噪声干扰的随机三种群食物链模型进行生存性分析，得到了全局正解的存在唯一性、最高级种群在均值意义下的持久性以及部分种群灭绝,并且其余种群均值意义下稳定持久性的判别准则.结果显示,Lévy跳可以明显地改变种群的生存状态,可使得持久的种群灭绝,也可使灭绝的种群持久.

关键词: 随机食物链模型, Lévy跳, 白噪声, 平均持久性, 灭绝性

Abstract: The survival of a stochastic three species food chain model with white noise and general Lévy jumps was analyzed, which includes existence and uniqueness of global positive solution as well as permanence in the mean of the highest species.Situations where some species are extinct while others are persistent in the mean were also clarified.The results show that Lévy jumps can obviously change the survival of population, which can make the persistent population become extinct, or vice versa.

Key words: stochastic food chain model, Lévy jumps, white noise, permanence in the mean, extinction

中图分类号:

O175.7

曾婷，滕志东. 带一般Lévy跳和白噪声干扰的随机三种群食物链模型的生存性分析[J]. 中国科学技术大学学报, 2018, 48(8): 622-630.

ZENG Ting, TENG Zhidong. Survival analysis of stochastic three-species food chain model with white noise and general Lévy jumps[J]. Journal of University of Science and Technology of China, 2018, 48(8): 622-630.

参考文献

［1］
HSU S B, HWANG T W, KUANG Y. A ratio-dependent food chain model and its applications to biological control[J]. Math Biosci, 2003, 181: 55-83.
[2] 李海红.随机种群模型的渐进行为[D].长春：吉林大学, 2014.
[3] SUN Y, SAKER S H. Positive periodic solutions of discrete three-level food-chain model of Holling type Ⅱ[J]. Appl Math Comput, 2006, 180: 353-365.
[4] GOH B S. Global stability in many-species systems[J] The American Naturalist, 1977, 111(977): 135-143.
[5] LIU M, BAI C. Analysis of a stochastic tri-trophic food-chain model with harvesting[J]. J Math Biol, 2016, 73: 597-625.
[6] BAO J, YUAN C. Stochastic population dynamics driven by Lévy noise[J]. J Math Anal Appl, 2012, 391: 363-375.
[7] LI M, GAO H, WANG B. Analysis of a non-autonomous mutualism model driven by Lévy jumps[J]. Discrete & Continuous Dynamical Systems - B, 2016, 21(4): 1189-1202.
[8] LIU M, WANG K. Stochastic Lotka-Volterra systems with Lévy noise[J]. J Math Anal Appl, 2014, 410: 750-763.
[9] LIU M, BAI C. Dynamics of a stochastic one-prey two-predator model with Lévy jumps[J]. Appl Math Comput, 2016, 284: 308-321.
[10] LIU Q, JIANG D, SHI N. Stochastic mutualism model with Lévy jumps[J]. Comm Nonl Sci Num Simul, 2016, 43: 78-90.
[11] ZHOU Y, YUAN S, ZHAO D. Threshold behavior of a stochastic SIS model with Lévy jumps[J]. Appl Math Comput, 2016, 275: 255-267.
[12] GE Q, JI G, XU J, et al. Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 462: 1120-1127.
[13] CHEN C, KANG Y. Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise[J]. Comm Nonl Sci Num Simul, 2017, 42: 379-395.
[14] MAO W, MAO X. On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps[J]. J Comput Appl Math, 2016, 301: 1-15.
[15] ZOU X,WANG K. Numerical simulations and modeling for stochastic biological systems with jumps[J]. Comm Nonl Sci Nume Simul, 2014, 19: 1557-1568.
[16] ZHANG X, WANG K. Stability analysis of a stochastic Gilpin-Ayala model driven by Lévy noise[J]. Comm Nonl Sci Nume Simul, 2014, 19(5): 1391-1399.
[17] WU R, ZOU X, WANG K. Asymptotic properties of stochastic hybrid Gilpin-Ayala system with jumps[J]. Appl Math Comput, 2014, 249: 53-66.
[18] JIANG D, SHI N, LI X. Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation[J]. J Math Anal Appl, 2008, 340: 588-597.
[19] LIPTSER R S. A strong law of large numbers for local martingales[J]. Stoch Inter J Prob Stoch Proc, 1980, 3: 217-228.
[20] MAO X, MARION G, RENSHAW E. Environmental Brownian noise suppresses explosions in population dynamics[J]. Stoch Proc Appl, 2002, 97: 95-110.

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带一般Lévy跳和白噪声干扰的随机三种群食物链模型的生存性分析

Survival analysis of stochastic three-species food chain model with white noise and general Lévy jumps

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