An Optimal Problem Research Of The Fishing Model Based On Taxation

Biological mathematics is a discipline between mathematics and biology. This subject studies and solves the problems in biology from the view of mathematics and mechanics, and combines the dynamical problems and mathematical thinking methods organically.The presented thesis mainly discusses the modeling problem for fishing systems and the optimal taxation policy problems on the basis of nonlinear dynamic system theory, optimal control theory and other related control theory.The main works are summarized as follows:Firstly, the formation, development and application of control theory and biological mathematics are introduced. And the formation and development of the biological economy theory, together with the application of the tax in the fishery development are expounded. Then a briefly introduction of basic knowledge is given as a foundation of the research.Secondly, fishing model based on the taxation is established in order to solve the equilibriums of the system. Then local stability in each equilibrium point and the global asymptotic stability of the positive equilibrium points are discussed. Numerical simulation using MATLAB is also given to verify the effectiveness of the conclusion.Thirdly, optimal problem of the fishery resources, the objective of which is to maximize the monetary social benefit as well as conservation of the ecosystem, is researched. Besides, some numerical simulations are given to illustrate our analytic results.Finally, we summarize the conclusion of the thesis and propose unresolved issues of it, which needed to do further research and exploration in the future.