In many spatial resource models it is assumed that the agent is able to determine the harvesting activity over the complete spatial domain. However, agents frequently have only access to a resource at particular locations at which the moving biomass, such as fish or game, may be caught or hunted. To analyse this problem, we set up a simple optimal control model of boundary harvesting. Using the Pontryagin’s Maximum Principle we derive the associated canonical system, and numerically compute canonical steady states and optimal time dependent paths, and characterise the optimal control and the associated stock of the resource. Finally, we extend our model to a predator-prey model of the Lotka-Volterra type, and show how the presence of two species enriches the results of our basic model. For both models we illustrate the dependence of the optimal steady states and the optimal paths on the cost parameters.

中文翻译：

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沿海捕捞的最佳渔业

在许多空间资源模型中，假设代理能够确定整个空间域的采伐活动。然而，代理通常只能访问特定位置的资源，在这些位置可以捕获或猎杀移动的生物量，例如鱼或猎物。为了分析这个问题，我们建立了一个简单的边界采集最优控制模型。使用庞特里亚金最大原理，我们推导出相关的规范系统，并数值计算规范稳态和最佳时间相关路径，并表征资源的最佳控制和相关存量。最后，我们将模型扩展到 Lotka-Volterra 类型的捕食者-猎物模型，并展示两个物种的存在如何丰富我们基本模型的结果。