Higher order dependency of chaotic maps


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 non-linear 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.

In International Symposium on Nonlinear Theory and its Applications (NOLTA)
Theodore Papamarkou
Theodore Papamarkou
Professor in maths of data science

Knowing is not enough, one must compute.