一类受分数Brown运动影响的资源竞争种群系统的渐近行为
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摘要
对一类n个种群,k个资源的随机资源竞争种群模型进行了研究(恒化器模型).其中种群的死亡率受外界环境噪声分数Brown运动的影响.通过构造Lyapunov函数,得到该模型中种群在均方意义下的持续性和灭绝性准则.通过数值算例对所得的结论进行了验证.
In this paper,the stochastic resource competitive population model of n species and k resources is studied(i.e.chemostat model),in which the species mortality rates are influenced by the fractional Brownian motion of extrinsic noise environment.By constructing a Lyapunov functional,the persistence and extinction criteria are derived in the mean square sense.Some examples are given to illustrate the effectiveness of the theoretical result.
In this paper,the stochastic resource competitive population model of n species and k resources is studied(i.e.chemostat model),in which the species mortality rates are influenced by the fractional Brownian motion of extrinsic noise environment.By constructing a Lyapunov functional,the persistence and extinction criteria are derived in the mean square sense.Some examples are given to illustrate the effectiveness of the theoretical result.
引文
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[2]Huisman J,Weissing F J.Biodiversity of plankton by species oscillations and chaos[J].Nature,1999,402(6760):407-410.
[3]Khan A A,Zytner R G,Feng Z.Establishing Correlations and Scale-Up Factor for Estimating the Petroleum Biodegradation Rate in Soil[J].Bioremediation Journal,2015,19(1):32-46.
[4]Monod J.La Technique De Culture Continue Theorie Et Applications[J].Selected Papers in Molecular Biology by Jacques Monod,1978(不详):184-204.
[5]Fang Y,Scheibe T D,Mahadevan R,et al.Direct coupling of a genome-scale microbial in silico model and a groundwater reactive transport model[J].Journal of Contaminant Hydrology,2011,122(1):96-103.
[6]Li B,Smith H L.Global dynamics of microbial competition for two resources with internal storage[J].Journal of Mathematical Biology,2007,55(4):481.
[7]Fowler A C,Winstanley H F,Mcguinness M J,et al.Oscillations in soil bacterial redox reactions.[J].Journal of Theoretical Biology,2014,342(3):33-38.
[8]Wei M.Exponential stability of numerical solutions to stochastic age-dependent population equations with Poisson jumps[J].International Journal of Computational&Mathematical Sciences,2011,6(1):28-33.
[9]Ma W,Zhang Q,Wang Z.Asymptotic stability of stochastic age-dependent population equations with Markovian switching[J].Elsevier Science Inc,2014,227:309-319.
[10]申芳芳,辛志贤,张启敏,等.与年龄相关的随机种群系统分裂倒向Euler法的几乎必然指数稳定性[J].河南师范大学学报(自然科学版),2017,45(2):8-13.
[11]Li D,Zhu Q.Comparison principle and stability of stochastic delayed neural networks with Markovian switching[J].Neurocomputing,2014,123:436-442.
[12]Khasminskii R.Stochastic modelling and applied probability[M].2ed.Berlin Heidelberg:Springer-Verlag,2012.