RESUMO
The recurrence analysis of dynamic systems has been studied since Poincaré's seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy (Smax). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood (ϵ-vicinity), turning the analysis free of the vicinity parameter. In addition, ϵ turns out to be a novel quantifier of dynamical properties itself. We apply Smax and the optimum ϵ to deterministic and stochastic systems. The Smax quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series.
RESUMO
We investigate the multifractal properties in the dynamics of domain walls of a ferromagnetic film. We apply the Multifractal Detrended Fluctuation Analysis method in experimental Barkhausen noise time series measured in a 1000-nm-thick Permalloy film under different driving magnetic field frequencies, and calculate the fluctuation function F_{q}(s), generalized Hurst exponent h(q), multifractal scaling exponent τ(q), and the multifractal spectrum f(α). Based on this procedure, we provide experimental evidence of multifractality in the dynamics of domain walls in ferromagnetic films and identify a rich and strong multifractal behavior, revealed by the changes of the scaling properties of over the entire Barkhausen noise signal, independently of the driving magnetic field rate employed in the experiment.
