How do you if know a system displays chaotic behaviour or bifurcation? What tools can we use to find out? What is the best tool to solve and plot the systems with chaos and bifurcation?
Indicator of chaos is the Lyapunov exponents and fractal dimension. Tool for their construction - TISEAN. This is for analysis.
I basically publications in Russian.
Here is the code of how to use the tool to analyze chaos (p.51):
https://www.researchgate.net/publication/260953932_Identification_of_dynamical_systems_based_on_the_symmetry_of_the_reconstructed_attractors?ev=prf_pub
Generation of Chaos is a different task.
Book Identification of dynamical systems based on the symmetry of...
XTo plot chaotic systems, I prefer to use MATLAB. Thereare. Many free tools and cods online that can easily solve chaotic systems written in d language
Dear Evgeny Nikulchev and Samuel Ogunjo Thank you for your useful answers..
The orbit of dynamical system of initial point determines or test the chaos. Fractal is not chaos, it is stable dynamic ,but chaos is not stable. chaos not converges to unique point.
If the system is smooth you can do it with Matlab implementation, the software auto or matcont to find the different bifurcations; but if the system that you will study is piece wise-smooth you should do it with a event driven scheme. There are some authors that work in this field, like Mario di Bernardo or Gerard Olivar Tost that let us undertand phenomena like discontinous induced bifurcations or chaos.
Another numerical way is resorting to Poincare' sections. For smooth systems there are many tools. Among them I co-developed the library BAL, that can be freely downloaded from http://sourceforge.net/projects/biflib/
Hope this helps!
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