价格成本变化的Gompertz系统的捕获问题

Harvesting in gompertz system with variable price and cost

研究了具有Gompertz增长的生物种群 ,建立了价格成本变化的数学生物经济捕获模型。利用常微分方程定性理论对模型进行定性分析 ,证明平衡点的存在性、局部稳定性及极限环的不存在性 ,给出了获得单位努力量最大利润的条件。

In this paper we study the biocenosis which possesses Gompertz growth and set up the harvesting model of mathematical bioeconomics with variable price and cost.By means of the qualitative analysis of the of the ordinary differential equation,we prove the existence of equilibrium point,local stability and unexistence of limit cycle.The condition of which maximizes profit of unit is obtained.