Scholarlink

<p>In this paper, we investigate a series of harvesting problems in a predator–prey system with Beddington–DeAngelis (B-D) type functional response, focusing on bioeconomic equilibrium, maximum sustainable total yield (MSTY), and optimal economic benefits. Research shows that under the independent harvesting strategy, the MSTY exists when the Hessian matrix of the yield function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Y(e_1,e_2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Y</mi> <mo stretchy="false">(</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is negative definite; under the synchronous harvesting strategy, the MSTY can exist when appropriate parameter values are chosen. By incorporating Bang-Bang control and singular control into harvesting strategies, the system converges to the optimal equilibrium state faster than the constant effort harvesting strategy. The study employs a control parameterization method and utilizes the MISER 3 software package to solve two types of optimal control problems. These findings provide a theoretical basis for biological resource management.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Optimal Harvesting Problems in a Predator–Prey Model with Beddington–DeAngelis Functional Response

  • 期刊论文

  • 发表日期：

    2026年8月1日

查看全文
  • Junfeng Lin,
  • Wensheng Yang

摘要

In this paper, we investigate a series of harvesting problems in a predator–prey system with Beddington–DeAngelis (B-D) type functional response, focusing on bioeconomic equilibrium, maximum sustainable total yield (MSTY), and optimal economic benefits. Research shows that under the independent harvesting strategy, the MSTY exists when the Hessian matrix of the yield function \(Y(e_1,e_2)\) Y ( e 1 , e 2 ) is negative definite; under the synchronous harvesting strategy, the MSTY can exist when appropriate parameter values are chosen. By incorporating Bang-Bang control and singular control into harvesting strategies, the system converges to the optimal equilibrium state faster than the constant effort harvesting strategy. The study employs a control parameterization method and utilizes the MISER 3 software package to solve two types of optimal control problems. These findings provide a theoretical basis for biological resource management.