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The generalized Beverton-Holt equation and the control of populations

机译：广义Beverton-Holt方程和总体控制

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This paper is devoted to the investigation of the positivity, stability and control of the solutions of a generalized Beverton-Holt equation arising in population dynamics which is potentially subject to bounded discontinuities at sampling instants due to the harvesting (i.e. fishing/hunting) quota and eventual independent consumption. Other generalizations are that the intrinsic growth rate and the environment carrying capacity gains are allowed to be time-varying sequences. The interpretation of the appearance of discontinuities in the solution is the presence of impulsive terms in the corresponding continuous-time differential equation. The parallel interpretation in ecology is that there are two different recruitment levels at each current sampling time due, firstly, to the evolution of the population driven by its intrinsic growth rate and the environment carrying capacity and, subsequently, a second level arises due to harvesting and independent consumption from the existing spawning stock of the population. The "left" recruitment level occurs immediately before each current sampling time while the "right" one occurs just after related to the sampling period size. By this reason, the mathematical formulation presented distinguishes between "left" and "right" sides of the sampling times. The control actions on the population stock and recruitment might be performed in a direct fashion either through the environment carrying capacity in close habitats gains or the harvesting quota in open air environments. Both actions may be combined in some open air habitats subject to some artificial control.
机译：本文致力于研究种群动态中出现的广义Beverton-Holt方程的解的正性，稳定性和控制性，由于收获（即捕鱼/狩猎）配额和最终独立消费。其他概括是，内在增长率和环境承载能力的增长被允许为随时间变化的序列。解决方案中不连续出现的解释是在相应的连续时间微分方程中存在脉冲项。生态学中的平行解释是，在每个当前采样时间都有两个不同的征聘水平，这首先是由于人口的内在增长率和环境承载力所驱动的种群演化，其次是由于收获而产生的第二水平以及从现有人口中产生的独立消费。 “左”募集级别紧接在每个当前采样时间之前，而“右”募集级别紧接在与采样周期大小相关之后。因此，提出的数学公式区分了采样时间的“左侧”和“右侧”。对种群数量和征募的控制行动可以直接方式进行，要么通过在近距离生境中获得环境承载力，要么在露天环境中进行。在某些人为控制的露天生境中，这两种行为可能会合并在一起。

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