01輸入常微分方程組

第一步，輸入演化博弈中的常微分方程組。

其中：

X（1）為演化博弈中一方的決策機率X

X（2）為演化博弈中另一方的決策機率Y

按照函式名儲存為.m的檔案，例如案例中儲存為”differential.m”的檔案。

The first step is to input the ordinary differential equations in the evolutionary game.

among them:

X(1) is the decision probability of one party in the evolutionary game X

X(2) is the decision probability Y of the other party in the evolutionary game

Save as a .m file according to the function name, such as the file saved as "differential.m" in the example.

02輸入畫圖主程式

第一個圖：博弈雙方策略的演化

對上述程式的解釋：

1.ODE45函式：求解微分方程組的數值解

[T,Y]=ode45('differential',[0 5],[i j])

'differential'：求解的函式名

[0 5]：T時間的區間

[i j]：初始值向量

2.Grid on :顯示座標軸網格線

3.y（：，1）中逗號前是行，逗號後是列，冒號表示從幾到幾。所以y（：，1）表示第一列的所有元素

y（：，1）相當於dx/dt

y（：，2）相當於dy/dt

4.儲存該程式，再執行

Explanation of the above procedure:

1. ODE45 function: solve numerical solutions of differential equations

[T,Y]=ode45('differential',[0 5],[i j])

'differential': the name of the function to be solved

[0 5]: T time interval

[i j]: Initial value vector

2.Grid on: display the grid lines of the coordinate axis

3. In y(:,1), before the comma is the row, after the comma is the column, and the colon indicates the number from the number to the number. So y(:,1) means all elements in the first column

y(:,1) is equivalent to dx/dt

y (:, 2) is equivalent to dy/dt

4.Save the program and run

畫出的演化圖形：

第二個圖：微分方程為dx/dt的策略方的演化過程

畫出的圖形：

第三個圖：微分方程為dy/dt的策略方的演化過程

畫出的圖形：

參考資料：百度百科、谷歌翻譯