共生种群的有限时间稳定性分析及最优捕获算法  

Finite-Time Stability Analysis and Optimal Harvesting Algorithm of Symbiotic Populations

作　　者：张双红[1] 徐袁媛 ZHANG Shuanghong;XU Yuanyuan(College of Mathematics and Computer,Jilin Normal University,Siping 136000,Jilin Province,China)

机构地区：[1]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《吉林大学学报（理学版）》2024年第6期1411-1418,共8页Journal of Jilin University:Science Edition

基　　金：吉林省创新创业人才基金(批准号:2023QN31);吉林省自然科学基金(批准号:YDZJ202301ZYTS157,20240304097SF);吉林省发展和改革委员会创新项目(批准号:2021C038-7).

摘　　要：针对共生种群在有限时间内的最优捕获问题,通过讨论共生种群的有限时间稳定性,并利用Pontryagin极大值原理及Hamilton函数方法,给出共生种群的最优捕获策略.首先,基于养殖过程的数据信息对共生生物生长过程建立非线性模型,并在保证生态环境平衡的条件下,深入分析共生生长过程和共生系统的有限时间稳定性,给出了严格的证明过程;其次,应用基于Lyapunov方法的Pontryagin极大值原理推导出一种最优采收方法,并得到了最优采收解的一般算法;最后,用仿真对比实验结果证明该算法的有效性.Aiming at the problem of optimal harvesting of symbiotic populations in finite time,we proposed the optimal harvesting strategy for symbiotic populations by discussing finite-time stability of symbiotic populations,utilizing Pontryagin maximum principle and Hamilton function method.Firstly,a nonlinear model of the growth process of symbiotic organisms was established based on the data information of the breeding process.Under the condition of ensuring the balance of ecological environment,the finite time stability of the symbiotic growth process and the symbiotic system was deeply analyzed,and a strict proof process was given.Secondly,an optimal harvesting method was derived by applying Pontryagin maximization principle based on Lyapunov method,and the general algorithm of optimal harvesting solution was obtained.Finally,the effectiveness of the proposed algorithm was proved by using simulation and comparative experimental results.

关 键 词：共生种群 水产养殖 有限时间稳定 最优捕获 Pontryagin极大值原理 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]