关于人口对外部扰动的复原力
On population resilience to external perturbations
摘要：
研究了周期环境或有界环境中的空间显式收获模型。该模式是由一个抛物型方程与空间相关的非线性Kolmogorov-Petrovsky-Piskunov型，和一个负的外部强迫项$-δ$。利用上下解方法和第一特征值的刻画，得到了一类线性椭圆算子稳定解的存在性、不存在性和稳定解个数的结果.我们还刻画了作为强迫项振幅函数的发展方程的渐近行为。特别地，我们定义了两个临界值$δ^*$和$δ_2$，使得如果$δ$小于$δ^*$，则种群密度收敛到“显著”状态，其处处高于某个小阈值，而如果$δ$大于$δ_2$，则种群密度收敛到“剩余”状态，其处处低于该小阈值。我们的研究结果是有用的研究环境破碎化和最大持续产量之间的关系。我们提出的数值结果的情况下，随机环境。
英文摘要：
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external forcing term $-δ$. Using sub- and supersolution methods and the characterization of the first eigenvalue of some linear elliptic operators, we obtain existence and nonexistence results as well as results on the number of stationary solutions. We also characterize the asymptotic behavior of the evolution equation as a function of the forcing term amplitude. In particular, we define two critical values $δ^*$ and $δ_2$ such that, if $δ$ is smaller than $δ^*$, the population density converges to a "significant" state, which is everywhere above a certain small threshold, whereas if $δ$ is larger than $δ_2$, the population density converges to a "remnant" state, everywhere below this small threshold. Our results are shown to be useful for studying the relationships between environmental fragmentation and maximum sustainable yield from populations. We present numerical results in the case of stochastic environments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
