MatLAB 中解时滞微分方程 怎么写？

这是matlab中dde23的例子，通过这个例子，应该能看懂dde23个参数的作用。直接复制后边的代码就可以输出图形。

%DDEX1 Example 1 for DDE23.

% This is a simple example of Wille' and Baker that illustrates the

% straightforward formulation, computation, and plotting of the solution

% of a system of delay differential equations (DDEs).

%

% The differential equations

%

%y'_1(t) = y_1(t-1)

%y'_2(t) = y_1(t-1)+y_2(t-0.2)

%y'_3(t) = y_2(t)

%

% are solved on [0, 5] with history y_1(t) = 1, y_2(t) = 1, y_3(t) = 1 for

% t <= 0.

%

% The lags are specified as a vector [1, 0.2], the delay differential

% equations are coded in the subfunction DDEX1DE, and the history is

% evaluated by the function DDEX1HIST. Because the history is constant it

% could be supplied as a vector:

% sol = dde23(@ddex1de,[1, 0.2],ones(3,1),[0, 5])

%

% See also DDE23, FUNCTION_HANDLE.

% Jacek Kierzenka, Lawrence F. Shampine and Skip Thompson

% Copyright 1984-2004 The MathWorks, Inc.

% $Revision: 1.2.4.2 $ $Date: 2005/06/21 19:24:16 $

sol = dde23(@ddex1de,[1, 0.2],@ddex1hist,[0, 5])

figure

plot(sol.x,sol.y)

title('An example of Wille'' and Baker.')

xlabel('time t')

ylabel('solution y')

% --------------------------------------------------------------------------

function s = ddex1hist(t)

% Constant history function for DDEX1.

s = ones(3,1)

% --------------------------------------------------------------------------

function dydt = ddex1de(t,y,Z)

% Differential equations function for DDEX1.

ylag1 = Z(:,1)

ylag2 = Z(:,2)

dydt = [ ylag1(1)

ylag1(1) + ylag2(2)

y(2) ]

可以借助于嵌套函数或匿名函数实现附加参数的传递，例如functionmainy0=[1.40.10.1]A=linspace(eps,10,20)Y=A*NaNforii=length(A)a=A(ii)y=ode45(@eq2,[0a],y0)Y(ii)=y(end,1)endplot(A,Y)functiondy=eq2(t,y)dy=y*0dy(1)=-(a*y(2))/(4*exp(a*t/4))dy(2)=-(a/4)*(exp(a*t/4))*(y(1)+0.5)+(a/4)*y(2)-y(3)*((exp(a*t/4))^2)dy(3)=4*y(2)endend但微分方程组似乎是刚性的，不过换用ode15s、ode23s等适合刚性系统的算法效果也不理想（可以调用ode*函数时不返回参数，观察求解的过程）。

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