scholarly journals Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Chuanfu Wang ◽  
Qun Ding
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Approximate Entropy ◽  
Chaotic Time Series ◽  
Pseudorandom Sequence ◽  
Periodic Behavior ◽  
Experimental Implementation ◽  
Sequence Generator

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 efficiently. 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.

scholarly journals Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

2002 ◽  
Vol 7 (1) ◽  
pp. 41-52 ◽  
Author(s):  
A. M. López Jiménez ◽  
C. Camacho Martínez Vara de Rey ◽  
A. R. García Torres
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Logistic Map ◽  
Direct Methods ◽  
Short Time Series ◽  
Direct Estimation ◽  
Non Linear ◽  
Short Time

The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation ofλstarting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

Local Adaptive Nonlinear Filter Prediction Model with a Parameter for Chaotic Time Series

2010 ◽  
Vol 44-47 ◽  
pp. 3180-3184
Author(s):  
Fen Fang ◽  
Hai Yan Wang ◽  
Zhou Mu Yang
Keyword(s):  
Time Series ◽  
Prediction Model ◽  
Gradient Descent ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Logistic Map ◽  
Predictive Performance ◽  
Nonlinear Filter ◽  
Chaotic Time Series ◽  
Proposed Model

In order to improve the predictive performance for chaotic time series， we propose a novel local adaptive nonlinear filter prediction model. We use a function with a parameter to build an adaptive nonlinear filter in this model, and we train this model with an adaptive algorithm, deduced by the minimum square-root-error criterion and the steepest gradient descent rule. We evaluate the proposed model using four well-known chaotic systems, namely Logistic map, Henon map, Lorenz system and Rosslor system. All the results show a remarkable increase in predictive performance, comparing with the local adaptive nonlinear filter prediction model.

scholarly journals The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1420
Author(s):  
Chuanfu Wang ◽  
Yi Di ◽  
Jianyu Tang ◽  
Jing Shuai ◽  
Yuchen Zhang ◽  
...  
Keyword(s):  
Secure Communication ◽  
Chaotic Map ◽  
Digital Circuit ◽  
Pseudorandom Sequence ◽  
Periodic Behavior ◽  
Output Sequence ◽  
Digital Devices ◽  
Theoretical And Numerical Analysis ◽  
Dynamic Degradation ◽  
Sequence Generator

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

A Web-Based Intelligent Educational Laboratory System for Forecasting Chaotic Time Series

2015 ◽  
pp. 110-135
Author(s):  
Utku Kose ◽  
Ahmet Arslan
Keyword(s):  
Artificial Intelligence ◽  
Time Series ◽  
Chaos Theory ◽  
Intelligent Systems ◽  
Chaotic Systems ◽  
Chaotic Time Series ◽  
Laboratory System ◽  
Web Based ◽  
Intelligent Water Drops Algorithm ◽  
Forecast Time

In the context of Chaos Theory and its applications, forecasting time series of a chaotic system is an attractive work area for the current literature. Many different approaches and the related scientific studies have been introduced and done by researchers since the inception of this working area. Newer studies are also performed in order to provide more effective and efficient approaches and improve the related literature in this way. On the other hand, it is another important research point to ensure effective educational approaches for teaching Chaos Theory and chaotic systems within the associated courses. In this sense, this chapter introduces a Web-based, intelligent, educational laboratory system for forecasting chaotic time series. Briefly, the system aims to enable students to experience their own learning process over the Web by using a simple interface. The laboratory system employs an Artificial Intelligence-based approach including a Single Multiplicative Neuron System trained by Intelligent Water Drops Algorithm in order to forecast time series of chaotic systems. It is possible to adjust parameters of the related Artificial Intelligence techniques, so it may possible for students to have some knowledge about Artificial Intelligence and intelligent systems.

Chaotic Characteristics of Workface Gas Emission Time-Series Data

2013 ◽  
Vol 340 ◽  
pp. 456-460 ◽  
Author(s):  
Mei Ying Qiao ◽  
Jian Yi Lan
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Chaotic Behavior ◽  
Chaotic Time Series ◽  
Point Of View ◽  
Series Data ◽  
Embedding Dimension ◽  
Minimum Entropy ◽  
Gas Emission ◽  
Emission Time

The chaotic time series phase space reconstruction theory based in this paper. First, the appropriate embedding dimension and delay time are selected by minimum entropy rate. Followed the chaotic behavior are analyzed by the use of the Poincare section map and Power spectrum of time series from the qualitative point of view. Based on NLSR LLE the quantitative study of the chaotic time series characteristics indicators is proposed. Finally, the gas emission workface of Hebi 10th Mine Coal is studied. The several analytical results of the above methods show that: the gas emission time-series data of this workface has chaotic characteristics.

ALGORITHM FOR EXACT LONG TIME CHAOTIC SERIES AND ITS APPLICATION TO CRYPTOSYSTEMS

2004 ◽  
Vol 14 (10) ◽  
pp. 3607-3611 ◽  
Author(s):  
SHUNJI KAWAMOTO ◽  
TAKESHI HORIUCHI
Keyword(s):  
Time Series ◽  
Logistic Map ◽  
Rational Numbers ◽  
Prime Numbers ◽  
Chaotic Time Series ◽  
High Dependency ◽  
Key Space ◽  
Long Time ◽  
Computer Environment ◽  
Numerical Generation

It is said that the numerical generation of exact chaotic time series by iterating, for example, the logistic map, will be impossible, because chaos has a high dependency on initial values. In this letter, an algorithm to generate them without the accumulation of inevitable round-off errors caused by the iteration is proposed, where rational numbers are introduced. Also, it is shown that the period of the chaotic time series depends on the rational numbers including large prime numbers, which are fundamentally related to the Mersenne and the Fermat prime ones. Since the time series are numerically regenerated by the proposed algorithm in an usual computer environment, it could be applied to cryptosystems which do not need the synchronization, and have a large key-space by using large prime numbers.

scholarly journals Dynamical properties of a novel one dimensional chaotic map

2022 ◽  
Vol 19 (3) ◽  
pp. 2489-2505
Author(s):  
Amit Kumar ◽  
◽  
Jehad Alzabut ◽  
Sudesh Kumari ◽  
Mamta Rani ◽  
...  
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Logistic Map ◽  
Maximal Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Chaotic Logistic Map

<abstract><p>In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu &gt; 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.</p></abstract>

scholarly journals Studying the Chaotic Dynamics Using Rossler-Chua Systems Combined with A Semiconductor Laser

2021 ◽  
pp. 2213-2221
Author(s):  
Raied K. Jamal ◽  
Falah H. Ali ◽  
Falah A-H. Mutlak
Keyword(s):  
Time Series ◽  
Semiconductor Laser ◽  
Dynamic Systems ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Chaotic Dynamic ◽  
Secure Communications ◽  
Wide Field ◽  
New Chaotic System

     In this paper, two different chaotic dynamic systems are coupled using a semiconductor laser to produce a new chaotic system. These two chaotic systems are Rossler and Chua systems. X-dynamic of Rossler system was coupled optically using optical fiber as a carrier of signal with x, y, and z-dynamics of Chua system. The results were analyzed and the behavior of Chua system was found to be changing in time series which, in turn, changed the attractor. The Chua attractor was converted from double scroll to single scroll. The results obtained from connecting two different systems in chaotic behavior showed a remarkable increase in the bandwidth of Chua system. This increase in bandwidth opens up a wide field for many applications, the most important of which is in the field of secure communications.

scholarly journals Wavelet characterization of hyper-chaotic time series

2018 ◽  
Vol 64 (3) ◽  
pp. 283 ◽  
Author(s):  
J. S. Murguía ◽  
H. C. Rosu ◽  
L. E. Reyes-López ◽  
M. Mejía-Carlos ◽  
C. Vargas-Olmos
Keyword(s):  
Time Series ◽  
Chaotic Systems ◽  
Chaotic Time Series ◽  
Wavelet Coefficients ◽  
Numerical Characterization

A wavelet scaling numerical characterization of time series based on the variance of the wavelet coefficients is used for three well-known four-dimensional and one five-dimensional hyper-chaotic systems. We report several scaling behaviors for the states of these hyper-chaotic systems.

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