带周期系数的捕食-被捕食模型的相关性质

Relevant Properties of Predator-prey Model with Periodic Coefficients

针对渔业捕捞的经济效益问题,讨论了一个与鱼类相关的带周期系数的捕食-被捕食模型,研究了该模型的动力学特征,以及在捕获条件下两个物种的最优收获策略问题。为了了解模型系统稳定的动力学特征,利用微分方程的上下解理论,得到了模型系统的周期解存在且唯一的充分条件,保证了周期解的稳定性;再从模型的持续性与永久存在性的角度考虑,得到影响模型系统永久性的条件;最后利用极大值原理得到了模型在捕获条件下的最优收获策略,目的是在保持生态系统稳定性的情况下,使得渔业的经济效益最大化,保证社会的经济效益,同时也保护生态环境.

Aiming at the economic benefits of fishing,a predator-prey model with periodic coefficients is discussed.The dynamic characteristics of the model and the optimal harvesting strategy of two species under capture conditions are studied.In order to understand the dynamic characteristics of the stability of the model system,the existence and uniqueness of periodic solutions of the model system are obtained by using the upper and lower solutions theory of differential equations.The sufficient condition guarantees the stability of the periodic solution.From the persistence and permanence of the model,the conditions affecting the permanence of the model system are obtained.Finally,the optimal harvesting strategy of the model under capture conditions is obtained by using the maximum principle.The purpose is to maximize the economic benefits of fisheries,ensure the economic benefits of society and protect the ecological environment while maintaining the stability of the ecosystem.