关键词: 种群动力学, Lotka-Volterra模型, 协同发展, Pontryagin极大值原理, 最优资源调控策略

Abstract: Aiming at the problems that there were  difficultes in dynamic optimization and lack of theoretical guidance for resource regulation in the collaborative development among comples enterprise entities, we proposed an improved Lotka-Volterra collaborative work model. Firstly, by introducing resource input as a control variable, we derived the conditions for the collaborative system to achieve stability in a finite time and the stability time function, and used the Pontryagin’s maximum principle and the Hamilton function method to obtain the optimal resource regulation strategy for maximizing the collaborative economic benefits. Secondly, by comparing the effectiveness and feasibility of simulation algorithm, we calculated the resource input ratio for two types of enterprise entities to achieve maximum economic benefits. The experimental results show that the proposed algorithm not only provides a new idea for predicting the collaborative work path among different enterprise entities, but also provides theoretical basis for formulating scientific industrial regulation strategies.

Key words: population dynamic, Lotka-Volterra model, collaborative development, Pontryagin’s maximum principle, optimal resource regulation strategy