Revisiting the box counting algorithm for the correlation dimension analysis of hyperchaotic time series

Abstract

We undertake the correlation dimension analysis of hyperchaotic time series using the box counting algorithm. We show that the conventional box counting scheme is inadequate for the accurate computation of correlation dimension ( D 2) of a hyperchaotic attractor and propose a modified scheme which is automated and gives better convergence of D 2 with respect to the number of data points. The scheme is first tested using the time series from standard chaotic systems, pure noise and data added with noise. It is then applied on the time series from three standard hyperchaotic systems for computing D 2. Our analysis clearly reveals that a second scaling region appears at lower values of box size as the system makes a transition into the hyperchaotic phase. This, in turn, suggests that correlation dimension analysis can also give information regarding chaos-hyperchaos transition.