Use of correlation dimension function in dynamic systems

Abstract

A single fractal number cannot fully describe the complex structure of a strange attractor embedded in phase space of dynamic systems. Hence it is essential to seek a procedure through which fractal dimension provides more information about the underlying dynamic system, in order to serve such a purpose correlation integrals are calculated at every row or off-diagonal from the distance matrix obtained from a set of points on a strange attractor. The slope of each integral is plotted versus the number of row or off-diagonal considered in the calculation. Hence, an asymptotic convergence to correlation dimension is obtained in this manner. More information is revealed for the dynamic system including its lacunarity.