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A spatial food chain model for the Black Sea Anchovy, and its optimal fishery
Discrete and Continuous Dynamical Systems-Series B ( IF 1.2 ) Pub Date : 2020-12-07 , DOI: 10.3934/dcdsb.2020373 Mahir Demir , , Suzanne Lenhart ,
Discrete and Continuous Dynamical Systems-Series B ( IF 1.2 ) Pub Date : 2020-12-07 , DOI: 10.3934/dcdsb.2020373 Mahir Demir , , Suzanne Lenhart ,
We present a spatial food chain model on a bounded domain coupled with optimal control theory to examine harvesting strategies. Motivated by the fishery industry in the Black Sea, the anchovy stock and two more trophic levels are modeled using nonlinear parabolic partial differential equations with logistic growth, movement by diffusion and advection, and Neumann boundary conditions. Necessary conditions for the optimal harvesting control are established. The objective for the problem is to find the spatial optimal harvesting strategy that maximizes the discounted net value of the anchovy population. Numerical simulations using data from the Black Sea are presented. We discuss spatial features of harvesting and the effects of diffusion and advection (migration speed) on the anchovy population. We also present the landing of anchovy and its net profit by applying two different harvesting strategies.
中文翻译:
黑海An鱼的空间食物链模型及其最佳渔业
我们提出有界域上的空间食物链模型,结合最佳控制理论来研究收获策略。受黑海渔业的推动,利用非线性抛物线偏微分方程对log鱼种群和两个以上的营养水平进行了建模,该方程具有对数增长,通过扩散和对流运动以及诺伊曼边界条件。建立了最佳收获控制的必要条件。该问题的目的是找到使optimal鱼种群的折现净值最大化的空间最优收获策略。提出了使用来自黑海的数据进行的数值模拟。我们讨论了收获的空间特征以及diffusion鱼种群的扩散和对流(迁移速度)的影响。
更新日期:2020-12-15
中文翻译:
黑海An鱼的空间食物链模型及其最佳渔业
我们提出有界域上的空间食物链模型,结合最佳控制理论来研究收获策略。受黑海渔业的推动,利用非线性抛物线偏微分方程对log鱼种群和两个以上的营养水平进行了建模,该方程具有对数增长,通过扩散和对流运动以及诺伊曼边界条件。建立了最佳收获控制的必要条件。该问题的目的是找到使optimal鱼种群的折现净值最大化的空间最优收获策略。提出了使用来自黑海的数据进行的数值模拟。我们讨论了收获的空间特征以及diffusion鱼种群的扩散和对流(迁移速度)的影响。