solving system of ODE until equilibrium for different parameter values

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Asaf il 25 Lug 2014

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Commentato: Torsten il 22 Giu 2016

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 il 21 Giu 2016

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

Torsten il 22 Giu 2016

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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