How to find equilibrium points of a system of 5 non linear ordinary differential equations???
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I have a system of 5 non linear ordinary differential equations with variable coefficients (with at least 3 parameters that are unknown and rest of them are known). I am trying to find the equilibrium points by hand but it seems like it is not possible without the help of a numerical method. What would be a good method to calculate equilibrium points of the system? (I saw thousands of examples on internet but they use systems of two dimensional ODEs with constant coefficients, which seems to be the 'easiest' case..)
Another question (somehow related to the problem above): Would it be possible to check the stability of the equilibrium points and then draw a bifurcation diagram? If so, please suggest some way out!
Thank you very much for taking time out of your busy schedule to read/ answer my question! Really appreciated!
Alan Weiss on 22 Nov 2013
Edited: Alan Weiss on 22 Nov 2013
Basically you want to find a point where the derivative of each equation is zero. I mean, if your equations are
d/dt x(t) = F(x), where x and F are vectors of length N
then you are looking for a vector z such that F(z) = 0 (I mean the vector of all zero components). This is a job for fsolve.
MATLAB mathematical toolbox documentation