Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems. I. Second-order correlations and self similarity

Author

Rovatti, Riccardo ; Mazzini, Gianluca

Author_Institution

CEG-ARCES, Bologna Univ., Italy

Volume

49

Issue

2

fYear

2002

fDate

2/1/2002 12:00:00 AM

Firstpage

137

Lastpage

149

Abstract

A general approach is developed for the statistical analysis of quantized trajectories produced by a class of chaotic maps generalizing piecewise-affine Markov systems. The framework is based on a generalization of the Perron-Frobenius operator and on the mapping of its properties onto properties of tensor function algebra. The general results are specialized to the computation of second-order statistical behaviors and exemplified with the analysis of two nontrivial maps exhibiting self-similar correlation trends

Keywords

Markov processes; Z transforms; chaos; correlation theory; cryptography; discrete time systems; fractals; nonlinear dynamical systems; state-space methods; tensors; Perron-Frobenius operator; Z transform; algebraic singularity; causal systems; chaotic maps; closed-form expressions; complex numbers; factorization theorem; finite-state systems; fractals; higher-order correlation; macro-states; multilinear algebra; nontrivial maps; piecewise-affine Markov systems; probability densities; quantized trajectories; second-order correlation; second-order statistical behaviors; self-similar correlation trends; state space; symbolic dynamic tracking tensor; tensor function algebra; Algebra; Chaos; Chaotic communication; Fractals; Loss measurement; Markov processes; Quantization; Statistical analysis; Tensile stress; Trajectory;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.983862

Filename

983862