A Single Species Model with Impulsive Diffusion  

作　　者：JingHui Lan-sunChen 

机构地区：[1]DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200062,China&DepartmentofInformation&:ComputationSciences,GuangxiUniversityofTechnology,Liuzhou545006,China [2]DepartmentofAppliedMathematics,DalianUniversityofTechnology,Dalian,116024,China

出　　处：《Acta Mathematicae Applicatae Sinica》2005年第1期43-48,共6页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No.10171106)

摘　　要：In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.

关 键 词：impulsive diffusion stroboscopic map BOUNDEDNESS monotone concave map positive fixed point global stability 

分 类 号：O175.26[理学—数学]