solving system of ODE until equilibrium for different parameter values

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Asaf 2014-7-25

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https://ww2.mathworks.cn/matlabcentral/answers/143268-solving-system-of-ode-until-equilibrium-for-different-parameter-values

评论： Torsten 2016-6-22

I am trying to explore the equilibrium of a system of ODEs when tweaking different parameters. Currently, I have my ODE function (see SB1ode, below) and a function that calls the solver while passing the set of parameter values (SB1, below). I need help on how to tell the solver to stop at equilibrium, please, rather than at a fixed time. Thanks!

function [t,N] = SI1(s0,i0,Tmax,b,d,<more parameters>)
% Initial conditions
y0 = [s0 i0];
% parameters
P(1) = b;      
P(2) = d;      
P(3) = ... etc
% time steps
time = [0 Tmax];
% solve ODE system
[t,N] = ode45(@(t,Y) SI1ode(t,Y,P), time, y0);
end
function Y = SI1ode(t,x,P)
%parameters
b = P(1);      
d = P(2);      
...etc
%State variables
S = x(1);
I = x(2);
Y(1) = equation 1;
Y(2) = equation 2;
Y=Y';   %make column vector
end

And my running script is:

Tmax = 100;
s0 = 100;
i0 = 1e-2;
b = 2;      
...etc
D = [0 .01 0.05 0.1 0.15 0.2 0.3 0.4 0.5 .6 .7 .8 .9 1];
for j=1:length(D)
      d = D(j);
      [t,N] = SI1(s0,i0,Tmax,b,d,<more parameters>);
      result(j) = N(end,2)/(N(end,1)+N(end,2));
end

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Renee 2016-6-21

Did you ever find a solution? I am working on this problem too.

Torsten 2016-6-22

If you only search for the equilibrium state, use "fsolve" to solve for the stationary solution for your equations (i.e. delete the time derivatives).

Best wishes

Torsten.

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