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<p>Differential equations are essential tools for studying and managing fisheries resources. It can describe the pattern of changes in population size over time, including growth or decline trends, and provide the scientific basis for formulating management measures. This paper proposes an uncertain Fox equation by selecting a regulatory function of the rate of population increase, which corresponds to the Gompertz growth form. Then the solution of the uncertain Fox equation and the inverse uncertainty distribution of the solution are discussed. Based on the proposed uncertain Fox equation, three applications of the solution are also studied. Furthermore, the moment estimation based on residuals is applied to estimating the unknown parameters of the uncertain Fox equation, and a brief study of the cod population is provided. Finally, a paradox of the stochastic Fox equation is deduced.</p>

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Uncertain Fox equation

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Dan Chen,
  • Yang Liu

摘要

Differential equations are essential tools for studying and managing fisheries resources. It can describe the pattern of changes in population size over time, including growth or decline trends, and provide the scientific basis for formulating management measures. This paper proposes an uncertain Fox equation by selecting a regulatory function of the rate of population increase, which corresponds to the Gompertz growth form. Then the solution of the uncertain Fox equation and the inverse uncertainty distribution of the solution are discussed. Based on the proposed uncertain Fox equation, three applications of the solution are also studied. Furthermore, the moment estimation based on residuals is applied to estimating the unknown parameters of the uncertain Fox equation, and a brief study of the cod population is provided. Finally, a paradox of the stochastic Fox equation is deduced.