污染环境中具有Markov切换的随机互惠三种群生存分析
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摘要
研究污染环境下受到毒素和双重噪声(白噪声和有色噪声)作用的随机系统,建立污染环境中具有Markov切换的随机互惠三种群模型。利用随机微分方程相关理论和分析方法,考虑系统同时受到白噪声、有色噪声、毒素浓度及种群间相互作用因素对种群生存状态的影响,得到随机互惠三种群系统中各种群趋于灭绝、随机非平均持久、随机弱平均持久和随机强平均持久的充分条件。数值模拟验证了理论结果的正确性。
Consider the stochastic system with the effects of toxin and double noise(white noise and colored noise) in the polluted environment, and establish a stochastic cooperative three populations model with Markov switching. Taking white noise, colored noise, toxin concentration and the interaction between populations into account, the sufficient conditions of stochastic extinction, stochastic non-persistence in the mean, stochastic weak persistence in the mean and stochastic strong persistence in the mean for each population are obtained by the theory of stochastic differential equations and related analysis method. The correctness of theoretical results is tested through numerical simulation.
Consider the stochastic system with the effects of toxin and double noise(white noise and colored noise) in the polluted environment, and establish a stochastic cooperative three populations model with Markov switching. Taking white noise, colored noise, toxin concentration and the interaction between populations into account, the sufficient conditions of stochastic extinction, stochastic non-persistence in the mean, stochastic weak persistence in the mean and stochastic strong persistence in the mean for each population are obtained by the theory of stochastic differential equations and related analysis method. The correctness of theoretical results is tested through numerical simulation.
引文
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[7] WANG X H,JIA J W.Dynamic of a delayed predator-prey model with birth pulse and impulsive harvesting in a polluted environment [J].Physica A:Statistical Mechanics and its Applications,2015,422:1-15.
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[12] 刘思润,吕敬亮.一类随机互惠模型的渐近性质 [J].黑龙江大学自然科学学报,2016,33(2):162-169.
[13] 张笑玲,谢红梅.污染环境下三种群随机互惠系统生存分析 [J].黑龙江大学自然科学学报,2018,35(1):43-52.
[14] 王克.随机生物数学模型 [M].北京:科学出版社,2010:174-175.
[15] 张金.函数上、下极限与数列上、下极限关系的探讨 [J].高师理科学刊,2010,30(6):35-38.
[16] 卢天秀.拓扑空间中函数上(下)极限的一些性质 [J].四川理工学院学报,2011,24(3):264-266.
[2] HALLAM T G,CLARK C E,LASSITER R R.Effects of toxicants on populations:a qualitative approach I.equilibrium environmental exposure [J].ecological Modelling,1983,18(3-4):291-304.
[3] HALLAM T G,DE LUNA J T.Effects of toxicants on populations:a qualitative:approach III.environmental and food chain pathways [J].Journal of Theoretical Biology,1984,109(3):411-429.
[4] WANG W D,MA Z E.Permanence of populations in a polluted environment [J].Mathematical Biosciences,1994,122(2):235-248.
[5] 靳祯,马知恩.环境污染中三维Volterra系统持续生存与绝灭的阈值 [J].系统科学与数学,1998,18(3):366-370.
[6] 潘晋孝,王峰.环境污染中三维Volterra互惠系统持续生存与绝灭的阈值 [J].工程数学学报,2000,17(1):93-98.
[7] WANG X H,JIA J W.Dynamic of a delayed predator-prey model with birth pulse and impulsive harvesting in a polluted environment [J].Physica A:Statistical Mechanics and its Applications,2015,422:1-15.
[8] GARD T C.Stochastic models for toxicant-stressed populations [J].Bulletin of Mathematical Biology,1992,54(5):827-837.
[9] LIU M,WANG K.Survival analysis of a stochastic single-species population model with jumps in a polluted environment [J].International Journal of Biomathematics,2016,9(1):1-15.
[10] LIU M.Survival analysis of a cooperation system with random perturbations in a polluted environment [J].Nonlinear Analysis:Hybrid Systems,2015,18:100-116.
[11] ZHAO Y,YUAN S L,MA J L.Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment [J].Bulletin of Mathematical Biology,2015,77(7):1285-1326.
[12] 刘思润,吕敬亮.一类随机互惠模型的渐近性质 [J].黑龙江大学自然科学学报,2016,33(2):162-169.
[13] 张笑玲,谢红梅.污染环境下三种群随机互惠系统生存分析 [J].黑龙江大学自然科学学报,2018,35(1):43-52.
[14] 王克.随机生物数学模型 [M].北京:科学出版社,2010:174-175.
[15] 张金.函数上、下极限与数列上、下极限关系的探讨 [J].高师理科学刊,2010,30(6):35-38.
[16] 卢天秀.拓扑空间中函数上(下)极限的一些性质 [J].四川理工学院学报,2011,24(3):264-266.