关联色噪声对集合种群稳定性和平均灭绝时间的影响
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摘要
基于Levins模型的研究基础上,大量研究者对"集合种群"稳定性方面的问题进行了探讨,但是之前的大多数研究都局限于确定性Levins模型,或者只是单纯地在系统中加入理想的白噪声.本文根据经典的存在生境破坏的集合种群模型,分析了具有相同关联时间的色关联高斯色噪声对集合种群稳定性的影响,根据统一色噪声近似的方法,推导出集合种群模型的近似福克-普朗克方程(AFPE),在稳态情况下,得到系统稳态概率分布函数(SPDF)的解析解.应用最速下降法,得到系统的平均灭绝时间(MFPT)的解析表达式.对计算结果进行数值分析,最终的图像分析表明:(1)加性噪声强度D的增加导致Levins模型中集合种群稳定性被弱化,而乘性噪声强度Q的增加对Levins模型中集合种群的稳定性会产生不利影响;(2)τ的增加使集合种群的稳定性得到强化;(3)噪声正关联时(0<λ<1),|λ|的增大会增加集合种群的稳定性;而负关联时(-1<λ<0),|λ|的增大却会使集合种群的稳定性弱化;(4)平均灭绝时间T(x_s→x_0)是Q的减函数,Q的增加会促使集合种群平均灭绝时间减小;(5)T(x_s→x_0)是τ的单调增函数,τ的增加延缓集合种群的灭绝.
The concept of the metapopulation system was previously introduced by Levins.After that,many researchers have been studying in the field of metapopulation system based on the Levins model.However,most studies are limited to deterministic Levins model and white noises.In the paper,the mean extinction time and stability of a metapopulation system subjected to cross-correlated Gaussian colored noises are investigated based on the Levins model.By means of a unified colored-noise approximation approach(UCNA)and mathematical analysis,the Approximate Fokker-Planck equation(AFPE)of the Levins model is obtained,and the stationary probability distribution function(SPDF)is obtained by solving the FPE.And then,the analytical expression of the mean first-passage time(MFPT)of the Levins model is derived by using the steepest descent method.The numerical computations show that:1)The additive noise and the multiplicative noise intensity weaken the stability of metapopulation;2)τenhances the stability of metapopulation;3)in the case of 0<λ<1,the stability of the metapopulation is enhanced when the is|λ|increasing,but the stability is weakened in the case of-1<λ<0as|λ|increasing;4)the mean extinction time T(x_s→x_0)is a decreasing function of Q;5)The mean extinction time T(x_s→x_0)is an increasing function ofτ.
The concept of the metapopulation system was previously introduced by Levins.After that,many researchers have been studying in the field of metapopulation system based on the Levins model.However,most studies are limited to deterministic Levins model and white noises.In the paper,the mean extinction time and stability of a metapopulation system subjected to cross-correlated Gaussian colored noises are investigated based on the Levins model.By means of a unified colored-noise approximation approach(UCNA)and mathematical analysis,the Approximate Fokker-Planck equation(AFPE)of the Levins model is obtained,and the stationary probability distribution function(SPDF)is obtained by solving the FPE.And then,the analytical expression of the mean first-passage time(MFPT)of the Levins model is derived by using the steepest descent method.The numerical computations show that:1)The additive noise and the multiplicative noise intensity weaken the stability of metapopulation;2)τenhances the stability of metapopulation;3)in the case of 0<λ<1,the stability of the metapopulation is enhanced when the is|λ|increasing,but the stability is weakened in the case of-1<λ<0as|λ|increasing;4)the mean extinction time T(x_s→x_0)is a decreasing function of Q;5)The mean extinction time T(x_s→x_0)is an increasing function ofτ.
引文
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[27]杨慧涛,吴玉敏,张惠英.毒素作用下两种群时滞竞争系统的捕获分析[J].福州大学学报(自然科学版),2012(5):557-562.
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[29]王国威,程庆华,徐大海.色关联噪声对林木Logistic生长模型的影响[J].物理学报,2013,62(22):224208-224208.
[2]OTSO O.Habitat destruction,habitat restoration and eigenvector-eigenvalue relations[J].Mathematical Biosciences,2003,181(2):165-176.
[3]LEVINS R.Some demographic and genetic consequences of environmental heterogeneity for biological control[J].Bulletin of the Entomological Society of America,1969,15:237-240.
[4]HANSKI I,GILPIN M.Metapopulation biology:ecology,genetics and evolution[M].London:Academic Press,1996.
[5]周淑荣,王刚.保护区的大小和数量效果的模拟研究[J].生态科学,2002,21(3):193-196.
[6]SUSAN H.Local extinction in a metapopulation context:an empirical evaluation[J].Biological Journal of the Linnean Society,1991,42(1-2):73-88.
[7]MOILANEN A,HANSKI I.Metapopulation dynamics:effects of habitat quality and landscape structure[J].Ecology,1998,79(7):2503-2515.
[8]ALAN H,SUSAN H.Metapopulation dynamics and genetics[J].Annual Review of Ecology and Systematics,1994,25:167-188.
[9]HANSKI I.Metapopulation dynamics[J].Nature,1998,396(5):41-49.
[10]王参军,李江城,梅冬成.噪声对集合种群稳定性的影响[J].物理学报,2012,61(12):120506-120506.
[11]李江城,梅冬成.集合种群的延时效应[J].物理学报,2008,57(11):6792-6798.
[12]王康康,刘先斌,杨建华.色交叉关联噪声作用下集合种群的稳定性和平均灭绝时间[J].物理学报,2013,62(10):100502-100502.
[13]马祖飞,李典谟.种群统计随机性和环境随机性对种群灭绝的影响[J].生态学报,2003,23(12):2702-2710.
[14]胡岗.随机力与非线性系统[M].上海:上海科技教育出版社,1994:23.
[15]JUNG P,HANGGI P.Dynamical systems:a unified colored-noise approximation[J].Phys Rev A,1987,35(10):4464-4466.
[16]WANG C J,CHEN S B,MEI D C.Steady-state analysis of a bistable system subject to a colored multiplicative noise and white additive noise with colored cross-correlated noises[J].Chinese Physics,2006,15(7):1435-1440.
[17]王国威,徐大海,程庆华.关联噪声和周期信号驱动非对称双稳系统的稳态分析[J].量子电子学报,2014,31(1):86-93.
[18]GARDINER C W.Handbook of Stochastic Methods,Springer in Synergetics[M].Berlin:Springer-Verlag,1983.
[19]HU G,DITZINGER T,NING C Z et al.Stochastic resonance without external periodic force[J].Chinese Physics Letters,1993,71(6):807-810.
[20]VILAR J M G,RUBI J M.Stochastic multiresonance[J].Chinese Physics Letters,1997,78(15):2882-288.
[21]MCNAMARA B,WIESENFELD K.Theory of stochastic resonance[J].Physical Review A,1989,39(9):4854-4868.
[22]王国威,程庆华,徐大海.关联噪声对集合种群稳定性和平均灭绝时间的影响[J].华中师范大学学报(自然科学版),2014,48(2):190-196.
[23]CASTROF J,KUPERMAN M N,FUENTES M et al.Experimental evidence of stochastic resonance without tuning due to non-Gaussian noise[J].Physical Review E,2001,64(5):1051-1053.
[24]王国威,付燕.噪声在双稳和生物系统中非线性效应的应用研究[J].湖北理工学院学报,2016,32(3):46-51.
[25]BARZYKIN A V,SEKI K.Periodically driven linear system with multiplicative colored noise[J].Physical review E,1998,57(6):6555-6563.
[26]王国威.噪声作用下双稳系统和集合种群的统计性质研究[D].长江大学,2014.
[27]杨慧涛,吴玉敏,张惠英.毒素作用下两种群时滞竞争系统的捕获分析[J].福州大学学报(自然科学版),2012(5):557-562.
[28]JIA Y,LI J R.Transient properties of a bistable kinetic model with correlations between additive and multiplicative noises:Mean first-passage time[J].Phys Rev E,1996,53(6):5764-5768.
[29]王国威,程庆华,徐大海.色关联噪声对林木Logistic生长模型的影响[J].物理学报,2013,62(22):224208-224208.