A new algorithm for the analysis of strange attractors

Abstract

This work proposes a new algorithm aiming to locally measure the divergence of initially nearby trajectories. The divergence is considered in the case of strange attractors, as an alternative of classical Lyapunov exponents. The new algorithm makes use of the Euclidean distance in order to define the local divergence. It is, then, possible to analyze the geometry of the attractor through layers of same divergence, such as a tomography. The algorithm is applied, as an example, to the Colpitts chaotic oscillator.