University of Sydney
School of Mathematics and Statistics
School of Mathematics and Statistics, University of Sydney
A new test for chaos
Wednesday, September 17th, 2-3pm, Carslaw 173.
We describe a new test for determining whether a given deterministic
dynamical system is chaotic or nonchaotic. In contrast to the usual
method of computing the maximal Lyapunov exponent, our method is
applied directly to the time series data and does not require phase
space reconstruction. Moreover, the dimension of the dynamical system
and the form of the underlying equations is irrelevant. The input is
the time series data and the output is 0 or 1 depending on whether the
dynamics is non-chaotic or chaotic. The test is universally
applicable to any deterministic dynamical system, in particular to
ordinary and partial differential equations, and to maps.
Instead of looking directly at the base dynamics we construct a
group-extension which is fed by the dynamics. We can prove that
looking at this 'image' of the base dynamics on a plane is sufficient
to study the regularity or chaoticity of the base dynamics.