2012 MCM北美数学建模A题论文.doc

Mathematical model research on the nature of tea trees For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number13499 ? Problem ChosenA For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2012 Mathematical Contest in Modeling (MCM) Summary Sheet  Abstract: To better express a tree’s characteristic, furthermore to solve some actual problems. This paper used L system fractal model and Forest gap model to build an accurate and complete model to describe a tree position parameter and shape parameter. Our model is three steps: the intensity of the condition of the three model gradually diminish. First model, we use L system to create a tree without leaves. We then add leaf information to the first one which made it a complete tree. In model 3,we use forest gap model to add some more environmental factors, to amend the simulation to make it more real. To testify this model accuracy, we chose tea trees fudingdabai which are from Hunan province grown up from garden 13 years old canopy as our research object and testify the three models ,meanwhile calculate dispersion coefficient and the difference. From the dispersion we can know that the model is alright. After building the model, we did some research on the tree, use mathematical deformation to find the relations between the various parts of the tree, until at last get the weight of the tree. This paper specialized in layer modeling constructing , reducing the constraints , taking good advantage of matlab and spss, excel etc. to gradually to close to reality. Key words: L system fractal model, forest gap model, significance level testify, Layer modeling Contents 1. Introduction2 2. Analysis of the Problem… 2 3. Models…………… 4 4. Conclusions16 5. Future Work18 6. References19 I. Introduction To figure out the weight of all the leaves of a tree, we supposed that there are several factors that may inf