带时滞的单种群在n个斑块中持续生存的条件

Persisting Subsistence Condition of Single Species for Taking Delay in N-patches

对[2]中的单种群扩散模型进行了推广与改进,研究了fi(xi(t-τ))=ai(t)+di(t)(∑j=1xjnxj-1)n+ε+bi(t)xi(t-τ)-ci(t)xi2(t-τ)(i=1,2,…,n)与gi(xi(t-τ)=ai(t)+di(t)(∑j=1jnxj-1)-ε+bi(t)xi(t-τ)-ci(t)x2i(t-τ)(i=1,2,…,n)的正根存在性及种群密度函数的特性,利用数学分析的方法证明了在条件ai(t)≥εdi(t)下,该种群是持续生存的。

In this note, diffusion model of sigle species in [ 2 ] is extended. Existence of positive root on quadratic function fi（xi （ t -τ ） and gi （ xi （ t - τ） ） is studied. The quality of species density function is discussed. Utilizing the Mothed of Mathematics Analysis, the property that species is persisting subsistence is proved with the Condition ai（ t） ≥ εdi（ t） .