一个非能量最优控制问题的碎裂现象：Logistic扩散模型中总总体规模的优化
A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models
摘要：
在最近的一些工作之后，我们研究了关于资源分布的Logistic扩散模型的总总体规模的优化问题。利用空间异质性Fisher-KPP方程，我们得到了一个令人惊讶的碎片化现象：根据扩散率的尺度（即扩散率），最好是集中或碎片资源。我们的主要结果是，在域中的物种的扩散率越小，最优的资源分布趋于振荡。这与种群动力学中的其他标准形成鲜明对比，例如优化物种生存能力的经典问题，集中资源总是有利的，而不管扩散率如何。我们的研究是通过大量的数值模拟，证实我们的结果。
英文摘要：
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.
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