Dynamical properties of a novel one dimensional chaotic 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>

A New Parallel Fuzzy Multi Modular Chaotic Logistic Map for Image Encryption

This paper introduces a new image encryption algorithm based on a Parallel Fuzzy Multi-Modular Chaotic Logistic Map (PFMM-CLM). Firstly, a new hybrid chaotic system is introduced by using four parallel cascade chaotic logistic maps with a dynamic parameter control to achieve a high Lyapunov exponent value and completely chaotic behavior of the bifurcation diagram. Also, the fuzzy set theory is used as a fuzzy logic selector to improve chaotic performance. The proposed algorithm has been tested as a Pseudo-Random Number Generator (PRNG). The randomness test results indicate that system has better performance and satisfied all random tests. Finally, the Arnold Cat Map with controllable iterative parameters is used to enhance the confusion concept. Due to excellent chaotic properties and good randomization test results, the proposed chaotic system is used in image encryption applications. The simulation and security analysis indicate that this proposed algorithm has a very high security performance and complexity

Integrated Partial Encryption and Watermarking Technique for Digital Video using Chaos and Support Images

Encryption and Watermarking are image processing tools that are used mostly separately. Encrypting a document completely obscures it and watermarking is applied mostly for copy right protection. For entertainment type videos, partial encryption and watermarking may be integrated such that both objectives are attained. We report in this paper a novel combined partial encryption and watermarking algorithm for digital videos using chaotic system and support image. Watermarks are generated by using iris information of the authentic user or the authentic producer of the digital video. Watermarks of full size and half size are embedded in the luminance frame (s) of the video using simple LSB steganography. A sequence of color frames is watermarked in two phases, and partially encrypted in two layers, the watermarks considered are encrypted before embedding. The luminance frame (s) is (are) preprocessed before embedding with the watermarks to defy stega-analysis. Chaotic logistic map and a gray level support digital image is used for obtaining unique row/column sequences as well as for generating robust random binary sequences. A support color digital image is used in the first layer encryption of the digital video. Modified Rabinovich 4 dimensional hyper-chaotic system is used for second layer encryption. Encryption algorithm is applied in R, G, B frames separately. The technique may also be applied for integrated encryption and watermarking of digital images.

Alternated Chaotic Biogeography Based Algorithm for Optimization Problems

Chaotic maps have improved the performance of BBO algorithm as chaotic migration and chaotic mutation help in maintaining diversity of the population on a higher level to avoid a habitat's entrapment in the local optimal solutions. Many chaotic maps have been used in BBO algorithm. Recently, alternation method in discrete dynamics has emerged as a powerful tool for control and anti-control of chaos. In this article, it is proposed to use alternated chaotic logistic map in BBO algorithm to improve the performance further.