标题： 非局部扩散策略和异质环境对总种群的影响 显示英文标题

标题： Effects of nonlocal dispersal strategies and heterogeneous environment on total population

摘要： 在本文中，我们考虑以下具有非局部扩散策略的单种群模型$$ d\mathcal {L} [\theta] (x,t) + \theta(x,t) [m(x)- \theta(x,t)]=0 , $$，其中$\mathcal {L}$表示非局部扩散算子，并研究物种的扩散率和资源分布如何影响总种群数量。 首先，我们证明总种群与总资源之间的比率的上界为$C\sqrt{d}$。 此外，构造了例子以表明这个上界是最佳的。 其次，对于一种简化的非局部扩散算子，我们证明如果$ \frac{\sup m}{\inf m}<\frac{\sqrt{5}+1}{2}$，则总种群作为扩散率$d$的函数在$\displaystyle (\inf m, \sup m)$中恰好有一个局部最大值点。 这些结果揭示了局部和非局部扩散策略之间的本质差异。 显示英文摘要

摘要： In this paper, we consider the following single species model with nonlocal dispersal strategy $$ d\mathcal {L} [\theta] (x,t) + \theta(x,t) [m(x)- \theta(x,t)]=0 , $$ where $\mathcal {L}$ denotes the nonlocal diffusion operator, and investigate how the dispersal rate of the species and the distribution of resources affect the total population. First, we show that the upper bound for the ratio between total population and total resource is $C\sqrt{d}$. Moreover, examples are constructed to indicate that this upper bound is optimal. Secondly, for a type of simplified nonlocal diffusion operator, we prove that if $ \frac{\sup m}{\inf m}<\frac{\sqrt{5}+1}{2}$, the total population as a function of dispersal rate $d$ admits exactly one local maximum point in $\displaystyle (\inf m, \sup m)$. These results reveal essential discrepancies between local and nonlocal dispersal strategies.