具有Smith增长种群的时滞经济捕获模型

Delayed economic harvesting model for population with Smith growth

为了更真实地反映种群增长规律,该文建立了一类种群具有Smith增长的时滞经济捕获模型。利用时滞微分方程理论研究了系统平衡点的稳定性。分析了正平衡点的稳定性随时滞变化的开关现象。研究表明:时滞现象对平衡点的稳定性影响很大;当时滞增大时,稳定的平衡点会变成不稳定的,而正平衡点会出现稳定性的开关现象;当时滞足够大时,稳定的正平衡点最终会变为不稳定的;需要根据种群的时滞,适当控制捕获努力量,从而使得捕获努力量和种群的规模达到一个稳定的平衡状态。

To reflect the rule of population growth really,a delayed economic harvesting model for population with Smith growth is established. The stability of equilibriums is studied by the theory of delay differential equation. The stability switch of positive equilibriums with time delay is analyzed.The results show that the stability of equilibriums is influenced by time delay greatly; when the time delay increases,stable equilibriums may become instable,and positive equilibriums may switch; when the time delay is large enough,stable positive equilibriums become instable finally; the harvesting effort and the scale of the population reach a stable equilibrium state when the harvesting effort is controlled according to the time delay.