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Mathematical models of restoration and control of a single species with Allee effect

机译：具有Allee效应的单个物种恢复和控制的数学模型。

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摘要

According to the initial density of a single species with Allee effect and corresponding management strategy, three kinds of mathematical models are presented to describe the evolutionary process of the species by impulsive differential equations. When the initial density of the species is larger than economic injury level (EIL) (or economical threshold, ET), impulsive harvest control is considered in a finite time to decrease the population of the species. The feasibility of the impulsive harvest control in a finite time is given by the existence of solution of the model with initial and boundary value problem. When the initial density of the species is less than EIL (or ET), the model with state feedback control is formulated according to the state of the species. The existence and stability of periodic solution of the model with state feedback control are discussed. When the initial density of the species is less than the Allee threshold and the species tends to extinction, the model with impulsive release at fixed moments is presented to study the restoration of the species. The conditions for the feasibility of periodic restoration of the species are given. Finally, some discussions are given.
机译：根据具有Allee效应的单个物种的初始密度和相应的管理策略，提出了三种数学模型来描述基于脉冲微分方程的物种演化过程。当物种的初始密度大于经济损害水平（EIL）（或经济阈值ET）时，可以在有限的时间内考虑进行冲动性收获控制以减少物种的种群。通过存在初值和边值问题的模型的解的存在，给出了在有限时间内进行脉冲收获控制的可行性。当物种的初始密度小于EIL（或ET）时，将根据物种的状态制定具有状态反馈控制的模型。讨论了状态反馈控制模型周期解的存在性和稳定性。当物种的初始密度小于Allee阈值且物种趋于灭绝时，提出具有固定时刻脉冲释放的模型，以研究物种的恢复。给出了定期恢复该物种可行性的条件。最后，给出了一些讨论。

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  • 来源
    《Applied Mathematical Modelling》 |2010年第11期|3264-3272|共9页
  • 作者

    Hongjian Guo; Lansun Chen; Xinyu Song;

  • 作者单位

    Department of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, PR China Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;

    rnDepartment of Applied Mathematics, Dalian University of Technology, Dalian 116024, PR China;

    rnDepartment of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, PR China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    impulsive effect; boundary value problem; impulsive differential equation; single species; allee effect;

    机译：冲动效果边值问题;脉冲微分方程单种阿利效应;

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