论文标题
非能源最佳控制问题的碎片现象：在物流扩散模型中的总人口大小优化
A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models
论文作者
论文摘要
在最近的一些工作之后，我们研究了相对于资源分布优化物流扩散模型的总人口大小的问题。使用空间异质的Fisher-KPP方程，我们获得了令人惊讶的碎片现象：取决于扩散率的规模（即分散率），浓缩或碎片资源更好。我们的主要结果是，域中该物种的分散率越小，最佳资源分布往往会振荡。这与人口动态中的其他标准形成鲜明对比，例如优化物种的生存能力的经典问题，在该物种的生存能力中，集中资源始终是有利的，无论扩散性如何。我们的研究由众多数值模拟完成，这些模拟证实了我们的结果。
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a surprising fragmentation phenomenon: depending on the scale of diffusivity (i.e the dispersal rate), it is better to either concentrate or fragment resources. Our main result is that, the smaller the dispersal rate of the species in the domain, the more optimal resources distributions tend to oscillate. This is in sharp contrast with other criteria in population dynamics, such as the classical problem of optimising the survival ability of a species, where concentrating resources is always favourable, regardless of the diffusivity. Our study is completed by numerous numerical simulations that confirm our results.
