基于税收的渔业捕捞模型的最优问题的研究

发布时间：2018-04-12 12:44

本文选题：生物数学 + 税收　；参考：《东北大学》2014年硕士论文

【摘要】：生物数学是一门介于数学与生物学之间的学科,它从数学和力学的角度,研究和解决了生物学上的问题,并且把动力学问题与数学的思维方法进行了有机的结合。本文应用非线性动力系统理论,最优控制理论以及相关控制理论,研究了渔业捕捞系统的模型建立以及最优税收策略问题。本文主要工作包括以下几个方面：首先,本文主要介绍了控制理论和生物数学的形成、发展与应用,并阐述了生物经济理论的形成与发展,以及税收在渔业发展中的应用,又对一些基础知识进行了简要的介绍。其次,建立了基于税收的渔业捕捞模型,求解系统的平衡点,分别讨论了各个平衡点的局部渐近稳定性及正平衡点的全局渐近稳定性。利用MATLAB软件对模型进行数值模拟,以验证结论的正确性。再次,研究了渔业资源的最优问题,研究了种群资源的开发、调节和征税管理的问题。应用庞特里亚金极大值原理相关知识求得了最优税收策略,在该税收策略下,社会收入的贴现值达到最大,进而得到最优生物经济平衡点。利用MATLAB数值模拟的方法验证理论分析的结果。最后,对本文的结论进行概括和总结,并提出仍有很多问题尚未解决,需要在今后的工作中做进一步的研究和探索。
[Abstract]:Biomath is a subject between mathematics and biology. It studies and solves the biological problems from the angle of mathematics and mechanics, and organically combines the dynamic problem with the thinking method of mathematics.In this paper, nonlinear dynamic system theory, optimal control theory and related control theory are used to study the modeling of fishing system and the optimal tax policy.The main work of this paper includes the following aspects: firstly, this paper mainly introduces the formation, development and application of control theory and bio-mathematics, and expounds the formation and development of bio-economic theory, as well as the application of taxation in fishery development.Some basic knowledge is also briefly introduced.Secondly, a tax-based fishing model is established to solve the equilibrium point of the system. The local asymptotic stability of each equilibrium point and the global asymptotic stability of the positive equilibrium point are discussed respectively.The MATLAB software is used to simulate the model to verify the correctness of the conclusion.Thirdly, the optimization of fishery resources is studied, and the exploitation, regulation and tax management of population resources are studied.The optimal tax policy is obtained by using the relevant knowledge of Ponteriagin's Maxima principle. Under the tax policy, the discounted value of social income reaches the maximum, and the optimal equilibrium point of biological economy is obtained.The results of theoretical analysis are verified by MATLAB numerical simulation.Finally, the conclusion of this paper is summarized and summarized, and it is pointed out that there are still many problems to be solved, which need to be further studied and explored in the future work.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F812.42;F326.4;O224

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