Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient

This paper addresses the generalized synchronization of stochastic discrete chaotic systems with Poisson distribution coefficient. Firstly, based on the orthogonal polynomial approximation theory of discrete random function in Hilbert spaces, the discrete chaotic system with random parameter is transformed into its equivalent deterministic system. Secondly, a general method for the generalized synchronization of discrete chaotic system with random parameter is presented by Lyapunov stability theory and contraction theorem. Finally, two synchronization examples numerically illustrated that the proposed control scheme is effective for any stochastic discrete system

Research on digital image watermark encryption based on hyperchaos

The digital watermarking technique embeds meaningful information into one or more watermark images hidden in one image, in which it is known as a secret carrier. It is difficult for a hacker to extract or remove any hidden watermark from an image, and especially to crack so called digital watermark. The combination of digital watermarking technique and traditional image encryption technique is able to greatly improve anti-hacking capability, which suggests it is a good method for keeping the integrity of the original image. The research works contained in this thesis include: (1)A literature review the hyperchaotic watermarking technique is relatively more advantageous, and becomes the main subject in this programme. (2)The theoretical foundation of watermarking technologies, including the human visual system (HVS), the colour space transform, discrete wavelet transform (DWT), the main watermark embedding algorithms, and the mainstream methods for improving watermark robustness and for evaluating watermark embedding performance. (3) The devised hyperchaotic scrambling technique it has been applied to colour image watermark that helps to improve the image encryption and anti-cracking capabilities. The experiments in this research prove the robustness and some other advantages of the invented technique. This thesis focuses on combining the chaotic scrambling and wavelet watermark embedding to achieve a hyperchaotic digital watermark to encrypt digital products, with the human visual system (HVS) and other factors taken into account. This research is of significant importance and has industrial application value

Design and Implementation of Secure Chaotic Communication Systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal

Computational Intelligence and Complexity Measures for Chaotic Information Processing

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value

Lag, Anticipated, and Complete Synchronization and Cascade Control in the Dynamical Systems

We obtain the lag, anticipated, and complete hybrid projective synchronization control (LACHPS) of dynamical systems to study the chaotic attractors and control problem of the chaotic systems. For illustration, we take the Colpitts oscillators as an example to achieve the analytical expressions of control functions. Numerical simulations are used to show the effectiveness of the proposed technique

Design and implementation of secure chaotic communication systems

Chaotic systems have properties such as ergodicity, sensitivity to initial conditions/parameter mismatches, mixing property, deterministic dynamics, structure complexity, to mention a few, that map nicely with cryptographic requirements such as confusion, diffusion, deterministic pseudorandomness, algorithm complexity. Furthermore, the possibility of chaotic synchronization, where the master system (transmitter) is driving the slave system (receiver) by its output signal, made it probable for the possible utilization of chaotic systems to implement security in the communication systems. Many methods like chaotic masking, chaotic modulation, inclusion, chaotic shift keying (CSK) had been proposed however, many attack methods later showed them to be insecure. Different modifications of these methods also exist in the literature to improve the security, but almost all suffer from the same drawback. Therefore, the implementation of chaotic systems in security still remains a challenge. In this work, different possibilities on how it might be possible to improve the security of the existing methods are explored. The main problem with the existing methods is that the message imprint could be found in the dynamics of the transmitted signal, therefore by some signal processing or pattern classification techniques, etc, allow the exposition of the hidden message. Therefore, the challenge is to remove any pattern or change in dynamics that the message might bring in the transmitted signal.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Review of Some Promising Fractional Physical Models

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.Comment: 38 pages, LaTe

Chaotic Control and Generalized Synchronization for a Hyperchaotic Lorenz-Stenflo System

This paper is devoted to investigate the tracking control and generalized synchronization of the hyperchaotic Lorenz-Stenflo system using the tracking model and the feedback control scheme. We suppress the chaos to unstable equilibrium via three feedback methods, and we achieve three globally generalized synchronization controls. Novel tracking controllers with corresponding parameter update laws are designed such that the Lorenz-Stenflo systems can be synchronized asymptotically. Moreover, numerical simulations are presented to demonstrate the effectiveness, through the contrast between the orbits before being stabilized and the ones after being stabilized