# How do I plot a bifurcation diagram with known dynamical equations of motion (> 3 dimension)?

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Rebeka on 10 Nov 2022
Commented: William Rose on 17 Nov 2022
I have equation of motions for a system.The system is given by,
d[y]/dt=[f(x,t,parameters)] where, [y] is say 5 dimensional. I want to see how the solution changes with parameter. How do I write a code for that? The system is non-linear. Earlier I tried to plot bifurcation tree diagram for the system by storing variable after each period,by changing the parameter gradually to observe period doubling bifurcation, but in some cases I find some discontinuities that I don't quite understand. Any reference on how to correctly plot bifurcation diagram would be appreciated. William Rose on 10 Nov 2022
1. To see if the system has reached a steady state, check y(:,1), y(:,2), ..., y(:,5) for multiple time points at the end of the simulation, to see if the vector y has stabilized.
I am attaching a recent publication (here, but may be paywalled), in which we published experimental and theoretical bifurcation diagrams for a complex system. Figures 4-9 are bifurcation diagrams in which the parameter on the horizontal axis is the frequency of external stimulation. This was a study of the repsonse of a non-linear optical system to external laser modulation. We did not do the bifurcaiton analysis as described above, because "steady state" meant a phase-locked solution, which was not a steady state in the traditional sense.
William Rose on 17 Nov 2022
@Rebeka, I'm sorry but I do not have more to deevote to theis problem. I hope others will assist you.