In bifurcation diagrams, generally, fixed points are plotted against a particular parameter. However, people also plot such diagrams using experimentally obtained time responses. I am not able to understand exactly what is plotted against that parameter using the time response. In some of the papers, the y-axis is labeled as 'Amplitude'. Can anyone elaborate on this? What is the standard or right way to plot a bifurcation diagram using time series for different values of parameter?
Hi Pranav,
One way is to plot the Poincaré section of the envelope of the experimental time response as a function of the bifurcation parameter.
I did something similar in this paper if you want to take a look:
Article Design and experimental study of a Nonlinear Energy Sink cou...
Best,
G.
It's NOT true that in bifurcation diagrams, fixed points are plotted vs. a control parameter: it's the whole time series(having discarded certain initial values, perhaps) that's plotted and from there it can be deduced that, for certain ranges the time series, once some transients have been identified, the series converges to a fixed point, a cycle-or an attractor.
What is, always, plotted is the time series of the quantity of interest, as a function of some ``control parameter''.
A simple matlab code to plot the bifurcation diagram in Rössler's system is attached down here.
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