Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Design of nonlinear observer for chaotic message transmission

Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2013Includes bibliographical references (leaves: 60-64)Text in English; Abstract: Turkish and Englishx, 64 leavesChaos is an interesting nonlinear phenomena that occurs in wide variety of fields. A significant amount of research was devoted to understanding chaos and its properties. After that, researchers focused on searching for possible application areas for chaos to utilize its properties. The need to increase the security of a communication system is considered as a perfect match for chaos and its several properties, yielding chaotic communication. In this thesis, chaotic communication is approached from a control theory perspective. Specifically, three nonlinear observers are designed to extract message encrypted in a chaotic communication signal. The design and stability analysis is presented for the first observer, and the other observers are presented as modifications to the first one. Extensive numerical simulations are performed to demonstrate the viability of the proposed observers. Robustness of the observers to noise, additive disturbances, and parametric mismatch, and security of the observers are demonstrated numerically

Entropy in Dynamic Systems

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed

Color image encryption based on chaotic shit keying with lossless compression

In order to protect valuable data from undesirable readers or against illegal reproduction and modifications, there have been various data encryption techniques. Many methods are developed to perform image encryption. The use of chaotic map for image encryption is very effective, since it increase the security, due to its random behavior. The most attractive feature of deterministic chaotic systems is he extremely unexpected and random-look nature of chaotic signals that may lead to novel applications. A novel image encryption algorithm based on compression and hyper chaotic map techniques is proposed. Firstly the image is decomposed into three subbands R, G, and B then each band is compressed using lossless technique. The generated chaotic sequences from the 3D chaotic system are employed to code the compressed results by employing the idea of chaotic shift encoding (CSK) modulation to encode the three bands to generate the encrypted image. The experiments show that the proposed method give good results in term of security, feasibility, and robustness

Fractional order chaotic systems and their electronic design

"Con el desarrollo del cálculo fraccionario y la teoría del caos, los sistemas caóticos de orden fraccionario se han convertido en una forma útil de evaluar las características de los sistemas dinámicos. En esta dirección, esta tesis es principalmente relacionada, es decir, en el estudio de sistemas caóticos de orden fraccionario, basado en sistemas disipativos de inestables, un sistema disipativo de inestable de orden fraccionario es propuesto. Algunas propiedades dinámicas como puntos de equilibrio, exponentes de Lyapunov, diagramas de bifurcación y comportamientos dinámicos caóticos del sistema caótico de orden fraccionario son estudiados. Los resultados obtenidos muestran claramente que el sistema discutido presenta un comportamiento caótico. Por medio de considerar la teoría del cálculo fraccionario y simulaciones numéricas, se muestra que el comportamiento caótico existe en el sistema de tres ecuaciones diferenciales de orden fraccionario acopladas, con un orden menor a tres. Estos resultados son validados por la existencia de un exponente positivo de Lyapunov, además de algunos diagramas de fase. Por otra parte, la presencia de caos es también verificada obteniendo la herradura topológica. Dicha prueba topológica garantiza la generaci´n de caos en el sistema de orden fraccionario propuesto. En orden de verificar la efectividad del sistema propuesto, un circuito electrónico es diseñado con el fin de sintetizar el sistema caótico de orden fraccionario.""With the development of fractional order calculus and chaos theory, the fractional order chaotic systems have become a useful way to evaluate characteristics of dynamical systems and forecast the trend of complex systems. In this direction, this thesis is primarily concerned with the study of fractional order chaotic systems, based on an unstable dissipative system (UDS), a fractional order unstable dissipative system (FOUDS) is proposed. Dynamical properties, such as equilibrium points, Lyapunov exponents, bifurcation diagrams and phase diagrams of the fractional order chaotic system are studied. The obtained results shown that the fractional order unstable dissipative system has a chaotic behavior. By utilizing the fractional calculus theory and computer simulations, it is found that chaos exists in the fractional order three dimensional system with order less than three. The lowest order to yield chaos in this system is 2.4. The results are validated by the existence of one positive Lyapunov exponent, phase diagrams; Besides, the presence of chaos is also verified obtaining the topological horseshoe. That topological proof guarantees the chaos generation in the proposed fractional order unstable dissipative system. In order to verify the effectiveness of the proposed system, an electronic circuit is designed with the purpose of synthesize the fractional order chaotic system, the fractional order integral is realized with electronic circuit utilizing the synthesis of a fractance circuit. The realization has been done via synthesis as passive RC circuits connected to an operational amplifier. The continuos fractional expansion have been utilized on fractional integration transfer function which has been approximated to integer order rational transfer function considering the Charef Method. The analogue electronics circuits have been simulated using HSPICE.

A Simple and Robust Gray Image Encryption Scheme Using Chaotic Logistic Map and Artificial Neural Network

A robust gray image encryption scheme using chaotic logistic map and artificial neural network (ANN) is introduced. In the proposed method, an external secret key is used to derive the initial conditions for the logistic chaotic maps which are employed to generate weights and biases matrices of the multilayer perceptron (MLP). During the learning process with the backpropagation algorithm, ANN determines the weight matrix of the connections. The plain image is divided into four subimages which are used for the first diffusion stage. The subimages obtained previously are divided into the square subimage blocks. In the next stage, different initial conditions are employed to generate a key stream which will be used for permutation and diffusion of the subimage blocks. Some security analyses such as entropy analysis, statistical analysis, and key sensitivity analysis are given to demonstrate the key space of the proposed algorithm which is large enough to make brute force attacks infeasible. Computing validation using experimental data with several gray images has been carried out with detailed numerical analysis, in order to validate the high security of the proposed encryption scheme

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

Fractional-order projection of a chaotic system with hidden attractors and its passivity-based synchronization

This paper presents the fractional-order projection of a chaotic system, which delivers a collection of self-excited and hidden chaotic attractors as a function of a single system parameter. Based on an integer-order chaotic system and the proposed transformation, the fractional-order chaotic system obtains when the divergence of integer and fractional vector fields flows in the same direction. Phase portraits, bifurcation diagrams, and Lyapunov exponents validate the chaos generation. Apart from these results, two passivity-based fractional control laws are designed effectively for the integer and fractional-order chaotic systems. In both cases, the synchronization schemes depend on suitable storage functions given by the fractional Lyapunov theory. Several numerical experiments confirm the proposed approach and agree well with the mathematical deductions

SciTech News Volume 71, No. 2 (2017)

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