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

Abstract: 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.

Key words: symbiotic population, aquaculture, finite-time stability, optimal harvesting, Pontryagin maximum principle