Applied Mathematics Seminar

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.