文章目錄

• 具有常時滯的 DDE
• • 編寫時滯代碼
  • 修改成自用的一階系統微分方程
  • 再改一個二階的

具有常時滯的 DDE

舉例為如下方程
$$\begin{array}{rl}{y}_1^{\prime }(t)& =y_1(t?1)\\ y_2^{\prime }(t)& =y_1(t?1)+y_2(t?0.2)\\ y_3^{\prime }(t)& =y_2(t?1)\end{array}$$

編寫時滯代碼

%% 測試求解常時滯微分方程 % Author: Zhao-Jichao % Date: 2021-07-05 clear clc%% Define Time-Delay lags = [1 0.2];tspan = [0 5]; sol = dde23(@ddefun, lags, @history, tspan);%% Draw Results plot(sol.x,sol.y,'-o') xlabel('Time t'); ylabel('Solution y'); legend('y_1','y_2','y_3','Location','NorthWest');%% DDE Function function dydt = ddefun(t,y,Z) % equation being solvedylag1 = Z(:,1);ylag2 = Z(:,2);dydt = [ylag1(1); ylag1(1)+ylag2(2); y(2)]; end %------------------------------------------- function s = history(t) % history function for t <= 0s = ones(3,1); end %-------------------------------------------

修改成自用的一階系統微分方程

$$\begin{array}{rl}{y}_1^{\prime }& =y_1(t?0.1)\\ y_2^{\prime }& =y_2(t?0.5)\end{array}$$

寫成了兩個并列的形式，方便對比最終的效果。

代碼如下

%% 測試求解常時滯微分方程 % Author: Zhao-Jichao % Date: 2021-07-05 clear clc%% Define Time-Delay lags = [0.1 0.5];tspan = [0 5]; sol = dde23(@ddefun, lags, @history, tspan);%% Draw Results plot(sol.x,sol.y,'-o') xlabel('Time t'); ylabel('Solution y'); legend('y_1','y_2','y_3','Location','NorthWest');%% DDE Function function dydt = ddefun(t,y,Z) % equation being solvedylag1 = Z(:,1);ylag2 = Z(:,2);dydt = [-ylag1(2); -ylag2(2)]; end %------------------------------------------- function s = history(t) % history function for t <= 0s = ones(2,1); end %-------------------------------------------

再改一個二階的

方程為：
$$\begin{array}{rl}{y}_1^{\prime }& =y_2(t?0.1)\\ y_2^{\prime }& =?2\\ y_3^{\prime }& =y_4(t?0.5)\\ y_4^{\prime }& =?2\end{array}$$

%% 測試求解常時滯微分方程 % Author: Zhao-Jichao % Date: 2021-07-05 clear clc%% Define Time-Delay lags = [0.1 0.5];tspan = [0 3]; sol = dde23(@ddefun, lags, @history, tspan);%% Draw Results plot(sol.x,sol.y) xlabel('Time t'); ylabel('Solution y'); legend('y_1','y_2','y_3','y_4','Location','NorthWest');%% DDE Function function dydt = ddefun(t,y,Z) % equation being solvedylag1 = Z(:,1);ylag2 = Z(:,2);dydt = [ylag1(2); -2;ylag2(4); -2;]; end %------------------------------------------- function s = history(t) % history function for t <= 0s = ones(4,1); end %-------------------------------------------

Ref: 時滯微分方程 — 示例

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