Higher order Dependency of Chaotic Maps

Lawrance, A.J. and Papamarkou, T. (2006) Higher order Dependency of Chaotic Maps. In: International Symposium on Nonlinear Theory and its Applications (NOLTA '06), Bologna, Italy, 11-14 Sep 2006, pp. 695-698.

Abstract

Some higher-order statistical dependency aspects of chaotic maps are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, is used to access nonlinear dependence of the maps under consideration. A simple analytical expression for the quadratic ACF has been found in the case of fully stretching piece-wise linear maps. A minimum bit energy criterion from chaos communications is used to motivate choosing maps with strong negative quadratic autocorrelation. A particular map in this class, a so-called deformed circular map, is derived which performs better than other well-known chaotic maps when used for spreading sequences in chaotic shift-key communication systems.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Papamarkou, Dr Theodore
• Authors: Lawrance, A.J., and Papamarkou, T.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Copyright Holders: Copyright © 2006 IEICE
• First Published: First published in Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA '06): 695-698
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher