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
Reader in maths of data science

My research interests span probabilistic machine learning, with a main focus on Bayesian deep learning, and topological deep learning.