Design, Circuitry Implementation And Application Of Multi-scroll Chaotic Generators

Chaotic signals are non-periodic, random-like and bounded signals that are generated in a deterministic manner. Chaotic systems, which produce chaotic signals, exhibit continuous broadband frequency spectrum, complex and unpredictable behavior, and sensitive dependence on the initial conditions. These interesting features of a chaotic system make it useful in areas such as secure communications, synchronous prediction, random bit generation, etc. Hence, chaos has been extensively discovered and intensively studied over the last two decades. Nowadays, theoretical design and circuitry implementation of various chaotic generators have been a key subject of nonlinear science. In particular, generating complex multi-scroll chaotic attractors by simple electronic circuits has seen rapid development. However, it is still rarely reported that delayed feedback circuitry system can generate multi-scroll chaos.This thesis addresses how to generate multi-scroll delayed chaotic attractors as well as their typical applications. The main contributions of the present dissertation are listed below.①The first two charpters review the fundamental concepts of chaotic dynamics and chaotic phenomena in nonlinear dynamical circuits, including some fundamental theories, design methodologies and circuitry implementations of multi-scroll chaotic generators.②The third chapter addresses the theoretical design and circuitry implementation of multi-scroll chaotic attractors based on delayed differential equations (DDEs). We have presented a multi-scroll chaotic generator based on famous physiological Mackey-Glass evolution equation, in which centrosymmetric piecewise linear function is employed as the activation function. The circuit can exhibit multi-scroll chaotic oscillations simply by adjusting the value of a single resistance. Moreover, By piecewise linearizing the axisymmetric activation function in Liao's system, a novel circuit is designed to exhibit a mono-scroll chaotic attractor. Furthermore, by shifting and scaling the above-mentioned axisymmetric activation function, the circuit can exhibit two-scroll chaotic attractor. The proposed chaotic circuits may be used as a delayed multi-scroll chaotic generator, as a chaotic neuron circuit unit, or even as a cell in delayed cellular neural networks.③Based on the previous work, the fourth chapter is dedicated to the study of new methods for generating more complex n×m grid scroll chaotic attractors. 1) We design a system of two first-order delayed differential equations as a chaotic generator, followed by its circuitry implementation. 2) We present a delayed chaotic model with n×m-scroll chaotic attractors. Circuitry implementation shows the scrolls of strange attractor extend along two directions and circuit exhibits 2×6 grid chaotic attractors. The above two methods for generating complex n×m grid scroll chaotic attractors are of practical importance.④The fifth chapter studies the synchronization and adaptive synchronization of delayed chaotic systems. Synchronization of chaos is a naturally occurring phenomenon where one system mimics dynamical behavior of another system in a precise manner. Chaotic synchronization scheme between two coupled identical delayed systems is discussed theoretically and experimentally. In fact uncertainties and parameters mismatch would have effect on the stability of process of synchronization between the chaotic oscillators. It is well known that it is difficult to determine some system parameters in advance. Most parametrical values are characterized by uncertainties related to experimental conditions (temperature, external electric and magnetic field) that can destroy or even break the synchronization. Such troubles can, to a certain extent, be tackled through adaptive synchronization. To our knowledge, adaptive synchronization between delayed chaotic systems has seldom been reported to date. How to adaptively snchronizing a class of delayed chaotic systems based on parameter identification is investigated. Using the Lyapunov second method, we design an adaptive controller and a parameter estimation law, which make the states of two delayed chaotic systems being globally asymptotically synchronized. Computer simulations illustrate the effectiveness of the proposed method.⑤The sixth chapter explores an application of chaotic circuits as random bit generators (RBGs). RBGs are used in many areas including computer simulations, numerical analysis, performance evaluation of computer algorithms, statistical sampling, watermark for image authentication and cryptography, etc. To speed up the generation of random bit stream, we propose a novel chaotic oscillator based on the well-known sinusoidal oscillator, which is very suitable for monolithic implementation and is capable of operating at very high frequencies. Subsequently, the novel circuit is utilized as a RBG. The bit streams so generated have passed the standard NIST SP 800-22 test suit.Finally, some possible applications of the proposed multi-scroll delayed chaotic systems are addressed and some questions are raised for further study.