Characterization of multiscroll attractors using Lyapunov exponents and Lagrangian coherent structures.

The present work aims to apply a recently proposed method for estimating Lyapunov exponents to characterize—with the aid of the metric entropy and the fractal dimension—the degree of information and the topological structure associated with multiscroll attractors. In particular, the employed methodology offers the possibility of obtaining the whole Lyapunov spectrum directly from the state equations without employing any linearization procedure or time series-based analysis. As a main result, the predictability and the complexity associated with the phase trajectory were quantified as the number of scrolls are progressively increased for a particular piecewise linear model. In general, it is shown here that the trajectory tends to increase its complexity and unpredictability following an exponential behaviour with the addition of scrolls towards to an upper bound limit, except for some degenerated situations where a non-uniform grid of scrolls is attained. Moreover, the approach employed here also provide...