scholarly journals Periodic Points of Asymmetric Bernoulli Shifts

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Yong-Guo Shi ◽  
Kai Chen ◽  
Wei Liao
Keyword(s):  
Bernoulli Shift ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Periodic Points ◽  
Complete Structure ◽  
Bounded Interval ◽  
Bernoulli Shifts ◽  
Piecewise Linear Chaotic Map

It is well-known that Sharkovskii’s theorem gives a complete structure of periodic order for a continuous self-map on a closed bounded interval. As a further study, a natural problem is how to determine the location and number of periodic points for a specific map. This paper considers the periodic points of asymmetric Bernoulli shift, which is a piecewise linear chaotic map.

GENERALIZED ARITHMETIC CODING USING DISCRETE CHAOTIC MAPS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250256 ◽  
Author(s):  
QIUZHEN LIN ◽  
KWOK-WO WONG ◽  
JIANYONG CHEN
Keyword(s):  
Chaotic Maps ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Interval Mapping ◽  
International Standards ◽  
Arithmetic Coding ◽  
Initial Value ◽  
Compression Performance ◽  
Piecewise Linear Chaotic Map ◽  
Generalized Arithmetic

Making use of the Lebesgue measure preserving property of the piecewise linear chaotic map, a discrete piecewise linear chaotic map is employed to perform the generalized arithmetic coding, which is an optimal entropy coding algorithm adopted by international standards. After a number of message symbols have been encoded by the reverse interval mapping, an enlargement on the encoding interval is performed and some codeword bits are exported accordingly. Based on the enlarged encoding interval, the subsequent symbols are encoded with the modified chaotic maps, the lower and upper bounds of which are determined by the final encoding interval of the symbols already encoded. In the decoding process, the message symbols are recovered by iterating the corresponding chaotic map from an appropriate initial value. The encoding interval enlargement is tracked by performing reverse interval mapping on the decoded symbols. More codeword bits are shifted into the register to form the initial value for decoding the subsequent symbols. Simulation results verify that the compression performance of our scheme is very close to the entropy bound and is comparable to traditional finite-precision arithmetic coding. In addition, cryptographic capability can be integrated into our scheme to make it a joint compression and encryption scheme. Its security is enhanced when compared with the existing schemes based on traditional arithmetic coding.

A Novel Joint for Image Encryption and Coding Using Piecewise Linear Chaotic Map

2016 ◽  
Vol 13 (10) ◽  
pp. 7137-7143
Author(s):  
Bin Wang ◽  
Shihua Zhou ◽  
Changjun Zhou ◽  
Xuedong Zheng
Keyword(s):  
Image Encryption ◽  
Binary Data ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Secret Key ◽  
Initial Value ◽  
Tent Map ◽  
Piecewise Linear Chaotic Map ◽  
Plain Image ◽  
Gray Level Image

Due to the features of chaotic maps, they are widely used into encrypting and coding information. Inspired by the tent map which is used to code and encrypt binary data, a novel joint for image encryption and coding based on piecewise linear chaotic map is proposed in this paper. We divide piecewise linear chaotic map into 256 parts according to the property of gray level image. In order to enhance the security of image, the image is subsequently encrypted by the piecewise linear chaotic map in which the secret key of image encryption is determined by the initial of chaotic map. This stage of image encryption possesses high key and plain-image sensitivities which results from the secret key related to plain-image. Finally, the encrypted image is coded by the piecewise linear chaotic map with a different initial value. The experimental results validate the effect of the proposed system and demonstrate that the encrypted and coded image is secure for transmission.

Deterministic stochastic resonance in a piecewise linear chaotic map

1998 ◽  
Vol 58 (6) ◽  
pp. 8009-8012 ◽  
Author(s):  
Sitabhra Sinha ◽  
Bikas K. Chakrabarti
Keyword(s):  
Stochastic Resonance ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Piecewise Linear Chaotic Map

A Novel Medical Image Tamper Detection and Recovery Scheme using LSB Embedding and PWLCM

2014 ◽  
Vol 6 (2) ◽  
pp. 1-22
Author(s):  
Lin Gao ◽  
Tiegang Gao
Keyword(s):  
Medical Image ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Visual Quality ◽  
Tamper Detection ◽  
Experimental Results ◽  
Least Significant Bit ◽  
Piecewise Linear Chaotic Map ◽  
Watermark Embedding ◽  
Recovery Scheme

A novel medical image tamper detection and recovery scheme based on Least Significant Bit (LSB) embedding and Piecewise Linear Chaotic Map (PWLCM) is proposed in the paper. To meet the demand of medical usage, the proposed scheme not only improved the precision of detection compared with block-wise scheme of watermark embedding, but also guaranteed the security of the scheme by applying PWLCM. To evaluate the proposed scheme, a former scheme proposed by Xiao et al is used for comparison; the two scheme's visual quality, accuracy of detection, recovery quality and security are tested during the experiment. The experimental results suggest that the proposed scheme meets the demand of visual quality and security for using in medical image tamper detection and recovery.

Chaotic Mutation Immune Evolutionary Programming for Voltage Security with the Presence of DGPV

2017 ◽  
Vol 6 (3) ◽  
pp. 721
Author(s):  
Sharifah Azma Syed Mustaffa ◽  
Ismail Musirin ◽  
Mohd. Murthada Othman ◽  
Mohd. Helmi Mansor
Keyword(s):  
Distributed Generation ◽  
Energy Demand ◽  
Voltage Stability ◽  
Environmental Concern ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Stability Index ◽  
Evolutionary Programming ◽  
Voltage Security ◽  
Piecewise Linear Chaotic Map

<p>Due to environmental concern and certain constraint on building a new power plant, renewable energy particularly distributed generation photovoltaic (DGPV) has becomes one of the promising sources to cater the increasing energy demand of the power system. Furthermore, with appropriate location and sizing, the integration of DGPV to the grid will enhance the voltage stability and reduce the system losses. Hence, this paper proposed a new algorithm for DGPV optimal location and sizing of a transmission system based on minimization of Fast Voltage Stability Index (FVSI) with considering the system constraints. Chaotic Mutation Immune Evolutionary Programming (CMIEP) is developed by integrating the piecewise linear chaotic map (PWLCM) in the mutation process in order to increase the convergence rate of the algorithm. The simulation was applied on the IEEE 30 bus system with a variation of loads on Bus 30. The simulation results are also compared with Evolutionary Programming (EP) and Chaotic Evolutionary Programming (CEP) and it is found that CMIEP performed better in most of the cases.</p>

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