混合週期因子的生長曲線建模

Abstract

在這篇論文中，我們引用“海岸綠提-水筆仔”的資料\n。我們的目的是要找到一個合適的函數去擬合這些資料，以及找到一個合適的微分方程式，使得該方程式的解是能夠擬合這些資料的。這樣的函數以及微分方程將能幫助我們更了解這筆資料的性質，並對預測資料未來走向更有幫助。\n\n我們首先藉由生長曲線來建構我們的數學函數，並對這個數學函數的模型加上週期項來改良。藉由Matlab curve fittig tool，我們找到了這個函數的一組參數來擬合原始資料。最後得到的結果如我們的預期，加了週期函數做出來的建模較原本生長曲線的建模更為貼近原始資料。\n\n在尋找微分方程系統的建模上，我們參考了文獻方法，並加以改良。然而這個新的微分方程式在加上週期項來改良之後卻沒辦法找到解析解，所以我們利用基因演算的方法來去尋找適合這個微分方程系統的參數，並搭配Heun`s method，RK2 method和RK4 method求出一些數值解。最後得到了一個比原參考文章更好的結果。

In this paper, we focus on the data from the website "Seacoast Green Bank-Kandelia`. There are two things we want to do for these data. First, we want to find a function which graph fits these data. Second, we want to find a differential equation such that its solution fits these data well. By exploring the function and the differential equation, we can understand more properties of these data.\n\nWe first build our mathematical function from Logistic curve and improve it by adding a periodic factor. By using Matlab curve fitting tools, we find parameters of this function which fit these data well. The final result is the same as our expectation. The model by adding a periodic factor fits the data better than the model of Logistic function.\n\nTo look for a differential equation, we follow the method in \\cite{rfspaper} and improve it. However, there is no analytical solution after adding a periodic factor into the model. Thus we use the method of a genetic algorithm to find suitable parameters of this differential equation. Moreover, we find the numerical solution by using Heun`s method, RK2 method and RK4 method. Finally, we get a better result than one in Ren-fa, Chen`s paper.