Abstract

A distributed renewable resource of any nature is considered on a two-dimensional sphere. Its dynamics is described by a model of the Kolmogorov–Petrovsky–Piskunov–Fisher type, and the exploitation of this resource is carried out by constant or periodic impulse harvesting. It is shown that, after choosing an admissible exploitation strategy, the dynamics of the resource tend to limiting dynamics corresponding to this strategy and there is an admissible harvesting strategy that maximizes the time-averaged harvesting of the resource.

中文翻译：

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永久和脉冲收获球体 KPP 模型中最大时间平均收获的存在性

摘要

任何性质的分布式可再生资源都被认为是在二维球体上。其动态由柯尔莫哥洛夫-彼得罗夫斯基-皮斯库诺夫-费舍尔类型的模型描述，并且该资源的开发是通过持续或周期性的脉冲收获进行的。结果表明，在选择了可接受的开发策略后，资源的动态趋向于限制与该策略相对应的动态，并且存在一个可最大化资源的时间平均收获的可接受的收获策略。