Research On The Age-dependent Problems Of One Dimension Bamboo Forest In Biology Evolution Systems

The paper is intended to discuss the existence,uniqueness and positivity of solutions of the linear model and of the nonlinear Bamboo forest evolution model in a determined condition, by characteristic-line and Schauder Fixed-point theorem. Then the existence of the optimal control is proved by the Maximizing Sequence and the Mazur theorem. Since bamboo shoots obtain the nature of budding without human cultivation, shooting time centerring in spring together with the different economic values between bamboos and shoots ,certain measures like proper control of the cutting rates as well as retention rate should be practiced so as to maintain healthy and sustainable development of bamboo forest. Finally, the existence of optimal control and a necessary condition for optimal solution are deduced . The main results include the following four aspects:1. In the first chapter, some common models of quantitative distribution structures are introduced ,and we also illuminate and analyze some researches on these forest models at home and abroad.Besides, we will show some basic knowledge that this paper will use.2. In the second chapter, we will deal with the following nonlinear biology evolution system :This chapter deals with the process of age and density structure for Class A Bamboo forest, and the distinction, compared with other scholars, resides in that , we take a cosmopolitan view that maximized economic value can be obtained with the aid of certain measures like the proper control of the cutting and retaining rates , apart from that , the nature of budding spontaneously included as well. In this chapter,we denote byβ(·)≥β₀> 0the afforestation retention rate shoots. By using a variety of techniques such as the methods of characteristic-line and Schauder Fixed-point theorem etc.,we will prove:(OP1):For any given effective retention rate shootsβ(? ) and the cut rateμ( x , t),the solution p ( x , t )of the forest system exist and is unique. And using the results obtained, we further concluded : (?)3. In the third chapter, we study the business cycle in the bamboo forest, the system to maximize the economic benefits of two control problems: (?)4. This chapter discusses bamboo area resources and application of computer simulation, firstly, examples of the bamboo resources in the simulation model:In order to achieve a computer simulation, the model is discrete: Model is discretized in the form of vector symbolizing algebraic equations and matrix signing matrix equations, and due simulation and calculation for bamboo forest resources is based on that.To conclude, the applications of computational animation applied in the management of bamboo forest resources are also taken into consideration.