具有Gauss白噪声和Lévy噪声的似然竞争模型分析
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摘要
研究了一个带有食饵庇护的随机似然竞争模型,采用Gauss白噪声和Lévy噪声来模拟环境的随机扰动.通过利用比较定理和伊藤公式,得到了随机模型存在全局正解的结论以及种群灭绝、均值稳定、均值强持续生存的阈值条件.研究结果表明无论是Gauss白噪声还是Lévy噪声对于种群的持续生长都是不利的,因此建模时很有必要考虑环境的随机变化.
A stochastic apparent competition model with prey refuge is studied, Gauss white noise and Lévy noise is adopted to simulate the random perturbation of environment. By virtue of comparison theorem and It?'s formula, the conclusion that the stochastic model has a global positive solution and the threshold conditions of extinction, stable in the mean, strong persistence in the mean for population are derived. The results show that whether Gauss white noise or Lévy noise is unfavorable for the sustainable growth of population, therefore, it is essential to consider the stochastic change of environment when constructing model.
A stochastic apparent competition model with prey refuge is studied, Gauss white noise and Lévy noise is adopted to simulate the random perturbation of environment. By virtue of comparison theorem and It?'s formula, the conclusion that the stochastic model has a global positive solution and the threshold conditions of extinction, stable in the mean, strong persistence in the mean for population are derived. The results show that whether Gauss white noise or Lévy noise is unfavorable for the sustainable growth of population, therefore, it is essential to consider the stochastic change of environment when constructing model.
引文
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[15] Liu Q,Chen Q.Asymptotic behavior of a stochastic non-autonomous predator-prey system with jumps[J].Appl Math Comput,2015,271:418-428.
[16] Liu M,Wang K.Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps[J].Nonlinear Anal,2013,85:204-213.
[17] Liu M,Wang K.Stochastic Lotka-Volterra systems with Levy noise[J].J Math Anal Appl,2014,410:750-763.
[18] Liu M,Wang K.Survival analysis of a stochastic cooperation system in a polluted environment[J].J Biol Systems,2011,19:183-204.
[19] Protter P,Talay D.The Euler scheme for Lévy driven stochastic differential equations[J].Ann Probab,1997,25:393-423.
[2] Banerji A,Morin P J.Trait-mediated apparent competition in an intraguild predator-prey system[J].Oikos,2014,123:567-574.
[3] Enge S,Nylund G M,Pavia H.Native generalist herbivores promote invasion of a chemically defended seaweed via refuge mediated apparent competition[J].Ecol Lett,2013,16:487-492.
[4] Recart W,Ackerman J D,Cuevas A A.There goes the neighborhood:apparent competition between invasive and native orchids mediated by a specialist florivorous weevil[J].Biol Invasions,2013,15:283-293.
[5] Blitzer E J,Welter S C.Emergence asynchrony between herbivores leads to apparent competition in the field[J].Ecology,2011,92:2020-2026.
[6] 杨兴云.具有Beddington-DeAngelis功能性反应的非自治似然竞争系统的动力学行为[D].长春:吉林大学,2010.
[7] 梁桂珍,陈静.一类具有扩散和混合时滞的非自治竞争系统的持久性分析[J].河南师范大学学报(自然科学版),2012,40(5):20-22.
[8] 高美.带有食饵庇护的三种群模型分析[D].哈尔滨:黑龙江大学,2016.
[9] Kar T K.Stability analysis of a prey-predator model incorporating a prey refuge[J].Commun Nonlinear Sci,2005,10:681-691.
[10] Huang Y,Chen F,Zhong L.Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge[J].Appl Math Comput,2006,182:672-683.
[11] Tao Y,Wang X,Song X.Effect of prey refuge on a harvested predator-prey model with generalized fuctional response[J].Commun Nonlinear Sci,2011,16:1052-1059.
[12] 郭冠华,马维军,盛晓娜.带有食饵庇护的似然竞争系统分析[J].黑龙江大学自然科学学报,2017,34(6):640-646.
[13] Bao J,Mao X,Yin G,et al.Competitive Lotka-Volterra population dynamics with jumps[J].Nonlinear Anal,2011,74:6601-6616.
[14] Bao J,Yuan C.Stochastic population dynamics driven by Lévy noise[J].J Math Anal Appl,2012,391:363-375.
[15] Liu Q,Chen Q.Asymptotic behavior of a stochastic non-autonomous predator-prey system with jumps[J].Appl Math Comput,2015,271:418-428.
[16] Liu M,Wang K.Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps[J].Nonlinear Anal,2013,85:204-213.
[17] Liu M,Wang K.Stochastic Lotka-Volterra systems with Levy noise[J].J Math Anal Appl,2014,410:750-763.
[18] Liu M,Wang K.Survival analysis of a stochastic cooperation system in a polluted environment[J].J Biol Systems,2011,19:183-204.
[19] Protter P,Talay D.The Euler scheme for Lévy driven stochastic differential equations[J].Ann Probab,1997,25:393-423.