Use of correlation dimension function in dynamic systems


Koçak K., ŞEN Z.

Proceedings of the 1997 IEEE International Symposium on Intelligent Control, İstanbul, Turkey, 16 - 18 July 1997, pp.379-382 identifier

  • Publication Type: Conference Paper / Full Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.379-382
  • Istanbul Medipol University Affiliated: Yes

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. 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.