Calculate steady state of a system of non-linear odes

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UserCJ on 3 Mar 2022
I'm trying to solve a system of non linear odes in Matlab as follows.
editparams %parameters
Tend = 50;
Nt = 100;
% Define RHS functions
RHS = @(t,x) ModelRHS(t,x,param); %anonymous function defining the set of odes
x0 =[0.03;0.05;0.085]; %Initial condition
t = linspace(0,Tend,Nt); %TSPAN
[t x] = ode45(RHS, t, x0);
I need to find the steady state of the system and I'm trying to create a function for this. Apart from that, I thought I'd use the Jacobian to identify stable and unstable steady states. My equations are in an anonymous function which is defined as `f` in the code below.
Can someone please help me to code the steady state function?
function SS = SteadyState(param, E)
f = @(t,x)ModelRHS(t,x,param,E); %set of odes
SymbolicSystem = sym(f); %trying to make the anonymous function symbolic
SymbolicJacobian = jacobian(SymbolicSystem',x); %jacobian
Jacob = matlabFunction(SymbolicJacobian,x);
Thanks in advance!
Bjorn Gustavsson
Bjorn Gustavsson on 4 Mar 2022
how could we possibly help with the information you've provided? We not absolutely nothing about your ODE-function except that it is non-linear. That is not sufficient to even start helping. What about just integrating the ODE numerically to see if it aproaches some steady-state level/behaviour?

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