Solution of DAE-System is too linear

Question

Georg Folwerk 2022-3-31

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1685564-solution-of-dae-system-is-too-linear

评论： Georg Folwerk 2022-3-31

Hi guys, I have a homework assignment where I am supposed to use DAE systems to describe the ecological balance of forest stand, grass stand, bird population and insect population. I have implemented this, but I don't like my solution. It all looks so linear, which it shouldn't, and the bird population and insect population is growing far too slowly.

The equations in the task are as follows:

% Variable declaration
tspan = linspace(t1, t2);
% DGL-declaration 
%x=x1; y=x2; z=x3
odefun = @(t,X) [ a*x*(1-(x/k))-h*x-f*y*(x/(x+d)); % DGL
                  b*y*(1-(y/(m*x*(k-x))))-g*z*(y/(y+e));
                  c*z*(1-(z/(n*x*y)))];
% Parameter declaration
x = 20; % Initial values
y = 0.001;
z = 0.0001;
conds = [x, y, z]; %Column vector for initial values (conditions)
% DGL solution
[t,X] = ode45(odefun, tspan, conds);
%plot the results

In case you are wondering where the insect population graph is, it is basically the bird population graph.

I hope you can help me find the error(s).

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Answer 1

Torsten 2022-3-31

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1685564-solution-of-dae-system-is-too-linear#answer_931589

在 MATLAB Online 中打开

a = ...;
b = ...;
c = ...;
k = ...;
h = ...;
f = ...;
d = ...;
m = ...;
g = ...;
e = ...;
n = ...;
odefun = @(t,x,y,z) [ a*x*(1-(x/k))-h*x-f*y*(x/(x+d)); % DGL
                      b*y*(1-(y/(m*x*(k-x))))-g*z*(y/(y+e));
                      c*z*(1-(z/(n*x*y)))];
x = 20; % Initial values
y = 0.001;
z = 0.0001;
conds = [x, y, z]; %Column vector for initial values (conditions)
t1 = ...;          % integration period
t2 = ...;
tspan = linspace(t1, t2);
% DGL solution
[t,X] = ode45(@(t,X)odefun(t,X(1),X(2),X(3)), tspan, conds);
plot(t,X)         % plot solution