GALI/SALI Method for chaos detection
Datseris opened this issue · comments
The Smaller and Generalized Alignment Indices methods are robust techniques that can distinguish chaotic behavior from regular, or stable periodic orbits from unstable ones, efficiently.
These efficient chaos indicators are based on the evolution of two or more, initially distinct, deviation vectors from a studied orbit. The methods are in general faster than computing maximum Lyaopunov exponents
In my eyes, the best literature to get this method from is the book "Chaos Detection and Predictability", Lecture Notes In Physics 915, Springer (Chapter 5).
For reference, these are the original publications related to the Issue:
(The following are to the best of my knowledge):
The first publication that introduced the Alingment Indices method is https://www.google.de/search?q=Skokos+Ch+2001+J.+Phys.+A:+Math.+Gen.+34+10029&ie=utf-8&oe=utf-8&gws_rd=cr&dcr=0&ei=AGnSWcHzFcqKgAbY3rCoDg
However, most known it became by this paper: http://iopscience.iop.org/article/10.1088/0305-4470/37/24/006/meta
Whereas the most known GALI paper is: http://www.sciencedirect.com/science/article/pii/S0167278907001273
I have implemented this but I am having trouble in the case of regular motion: the gali doesn't give a power law. everything else works perfectly including the 1/t^2 case of 2d maps. For chaotic orbits I get the lyapunov power law excellently.
Still, don't know why regualr motion in higher dimensions doesn't work. If someone is willing to help please reply here.