Quantifying chaos in continuous dynamical systems using the extended entropic chaos degree

Abstract

This study shows that the extended entropic chaos degree (EECD) can quantify the chaos of the Lorenz and Rössler equations under an adequate finite partition {A_i} of the domain. The Lyapunov exponent (LE) is often used to quantify chaos in dynamical systems. However, computing the LE is challenging when information about these systems is limited to time-series observational data. The EECD is a modified version of the original entropic chaos degree and is used as a criterion for measuring the strength of chaos from the perspective of information dynamics. The EECD can be directly computed from time-series data.