Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Abstract

When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved e ciently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

A novel method of constructing high-dimensional digital chaotic systems on finite-state automata*

“…[9] This phenomenon is called dynamical degradation, which may cause serious flaws in chaos-based applications. [10,11] Focusing on this problem, multiple remedies have been proposed to enhance chaotic systems and reduce the dynamical degradation, such as perturbing method (perturbation of chaotic states or control parameters), [12][13][14] integrating multiple chaotic systems (including cascading and switching methods), [15][16][17] or error compensation method. [18] Recently, Tutueva et al proposed a novel concept of chaotic maps with adaptive symmetry [19] and a two-parameter modified logistic map technique, [20] which both increase the length of chaotic orbits through introducing new parameters.…”