论文标题
散布物种的种群耗尽资源
Depletion of Resources by a Population of Diffusing Species
论文作者
论文摘要
自然和人工资源的消耗是一个基本问题，也是经济危机，生态灾难和生物体死亡的潜在原因。了解耗尽过程对于进一步控制和优化资源补充至关重要。在本文中，我们调查了一群物种种群的库存耗尽，这些物种在每次遇到股票时都会经历普通扩散并消耗资源。我们得出了随机耗竭时间的概率密度的确切形式，该时间耗尽了库存。该分布对物种数量，资源的初始数量和几何设置的依赖性进行了分析。讨论了未来的观点和相关的开放问题。
Depletion of natural and artificial resources is a fundamental problem and a potential cause of economic crises, ecological catastrophes, and death of living organisms. Understanding the depletion process is crucial for its further control and optimized replenishment of resources. In this paper, we investigate a stock depletion by a population of species that undergo an ordinary diffusion and consume resources upon each encounter with the stock. We derive the exact form of the probability density of the random depletion time, at which the stock is exhausted. The dependence of this distribution on the number of species, the initial amount of resources, and the geometric setting is analyzed. Future perspectives and related open problems are discussed.
