具有年龄结构的单种群模型的脉冲控制及其捕获策略

Impulsive Control of a the Stage-Structured Single-Species Model and Optimal Harvesting Policies

给出单种群阶段结构模型,利用脉冲微分方程的比较原理,通过状态反馈和输出反馈对模型变换后的系统进行了脉冲控制.对成年、幼年种群同时捕获,通过状态反馈,得到了单种群阶段结构模型在正平衡点渐近稳定的充分条件;通过输出反馈得到了相应的结论;并给出了脉冲控制时间间隔的上界估计值.分别对其幼年种群和成年种群捕获问题,给出以最大捕获可持续均衡收获(MSY)为目标的最优捕获策略.

According to the comparative theorem of Impulsive differential equations, the problem of impulsive control for a singe-species model with stage structure is investigated with state-feedback and output-feedback. By harvesting mature population and immature population, a sufficient condition which guarantees the asymptotical stability of the positive equilibrium is established with state-feedback. The corresponding result is obtained with output-feedback. For the impulsive controls which make the system asymptotically stable, the estimates of the upper bound of impulsive interval are obtained. It mainly studies the optimal harvesting policy of the single specie with age distribution when two stages are harvested respectively.