I have several time series, coming from a system that is stable and then unstable, I need to plot the bifurcation diagram using the time series. There is no ODE associated so MATLAB 1D Bifurcation is not useful. CAn anyone tell me a matlab code to do that?
Could you give more information about that Mr Toluwalope? Many thanks for the answer.
Hi Carlos,
The only way around your problem, as far as I can see it now, is to try to build a model from your data (time series), assuming you have the correct value of the bifurcation parameter for each of your time series. I think I've seen this in one of Prof. C. Letellier's papers (Physics Letters A, 1996... or something like that). This solution is far the best, and also quite "expensive", as it will require some experience in modelling from data.
Alternatively, if the number of your time series is sufficiently large, you can perform Poincaré sampling of the time series (make sure you discard all transients) and plot the resulting points against the bifurcation parameter, which I assume you have for each of your time series. In the end you will have a plot in which each time series will give rise to "something" along the y-axis for the particular value of bifurcation parameter, that you should indicate in the x-axis. If your data is a period-one limit cycle, your "something" along the y-axis will be just one dot (many dots in the same place), if it is a period P-limit cycle, you will have P dots along the y-axis for the particular value of the bifurcation parameter. If the data are chaotic you will have as many dots as number of cycles used, for the particular value of the bifurcation parameter.
As for RQA (Samuel Toluwalope's suggestion), this will only help if the time series already incorporates the bifurcation parameter variation. See, for instance, http://dx.doi.org/10.1016/j.physleta.2014.06.014 and references therein.
I am not aware of any code that will do this directly. You must built it yourself... step by step.
A Matlab toolbox for RQA is available at http://tocsy.pik-potsdam.de/CRPtoolbox/
http://tocsy.pik-potsdam.de/CRPtoolbox/
Many thanks. For your answers. The problem is that i have several time serires recorded from a system with some instability events. Some times they are evidents and clear, but other time not so far, but they are there. I´d like to know the moment in which the system jump form one state to the other state, and to know the limit cicle.
Luis Antonio Aguirre, it is true that a bifurcation parameter is needed. However, in a time series, using RQA can identify points at which changes occur in the time series. I am currently very busy now, else would have written a very simple working example. Norbert Marwan is a key figure in the use of RQA and would be able to shed more light on this.
Thanks
Hi Samuel,
yes, I agree entirely (see http://dx.doi.org/10.1016/j.physleta.2014.06.014). But RQA will give us the bifurcating instants, not a bifurcation diagram, if the data are nonstationary, as it seems to be the case. Carlos' second enquiry is more in this direction. He probably doesn't need a bifurcation diagram after all.
Cheers.
Thanks Guys for the answers i will try with the RQA in the first analysis but the question is still there, How to plot the bifurcation diagram from a time series.
Bifurcation diagram is the plot in which abscissa is the parameter, and ordinate is the dynamical variable. Each of time series corresponds to the one value of parameter, and you can to plot Poincare section of this time series on ordinate.
Perhaps what you need is wavelet analysis, which will identify changes in the power spectral density during the course of a single time series.
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