Impulsive Control and Synchronization of Chaos-Generating-Systems with Applications to Secure Communication

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area

Science's First Mistake

This book is available as open access through the Bloomsbury Open Access programme and is available on www.bloomsburycollections.com. The purpose of the book is to deconstruct the process of knowledge discovery and theory construction. Grounded in the tradition of second-order cybernetics, the concept of self-reference is used in the context of systems theory in order to examine the mode in which observation, paradox and delusion become 'structurally coupled' with cognition. To put this simply, physical scientists take it as a given that all the universe is explainable once we've discovered the underlying rules. Whereas social scientists and philosophers are more sensitive to the issues around how the observer actually impacts that which is being observed. The authors work in the fields of Information Studies, which is within the technical or physical realm, and Management Studies, which is about human behaviour. Their argument is that all scientists (physical and social) rely too much on the absolutism and certainty of the methods of traditional physical science and that we should acknowledge the limitations of how we know what we know. Rooted in information systems analysis this fresh and audacious examination of knowledge discovery and theory construction makes an important contribution to the understanding of how we employ scientific method

Science's First Mistake

This book is available as open access through the Bloomsbury Open Access programme and is available on www.bloomsburycollections.com. The purpose of the book is to deconstruct the process of knowledge discovery and theory construction. Grounded in the tradition of second-order cybernetics, the concept of self-reference is used in the context of systems theory in order to examine the mode in which observation, paradox and delusion become 'structurally coupled' with cognition. To put this simply, physical scientists take it as a given that all the universe is explainable once we've discovered the underlying rules. Whereas social scientists and philosophers are more sensitive to the issues around how the observer actually impacts that which is being observed. The authors work in the fields of Information Studies, which is within the technical or physical realm, and Management Studies, which is about human behaviour. Their argument is that all scientists (physical and social) rely too much on the absolutism and certainty of the methods of traditional physical science and that we should acknowledge the limitations of how we know what we know. Rooted in information systems analysis this fresh and audacious examination of knowledge discovery and theory construction makes an important contribution to the understanding of how we employ scientific method

Digital Signal Processing (Second Edition)

This book provides an account of the mathematical background, computational methods and software engineering associated with digital signal processing. The aim has been to provide the reader with the mathematical methods required for signal analysis which are then used to develop models and algorithms for processing digital signals and finally to encourage the reader to design software solutions for Digital Signal Processing (DSP). In this way, the reader is invited to develop a small DSP library that can then be expanded further with a focus on his/her research interests and applications. There are of course many excellent books and software systems available on this subject area. However, in many of these publications, the relationship between the mathematical methods associated with signal analysis and the software available for processing data is not always clear. Either the publications concentrate on mathematical aspects that are not focused on practical programming solutions or elaborate on the software development of solutions in terms of working ‘black-boxes’ without covering the mathematical background and analysis associated with the design of these software solutions. Thus, this book has been written with the aim of giving the reader a technical overview of the mathematics and software associated with the ‘art’ of developing numerical algorithms and designing software solutions for DSP, all of which is built on firm mathematical foundations. For this reason, the work is, by necessity, rather lengthy and covers a wide range of subjects compounded in four principal parts. Part I provides the mathematical background for the analysis of signals, Part II considers the computational techniques (principally those associated with linear algebra and the linear eigenvalue problem) required for array processing and associated analysis (error analysis for example). Part III introduces the reader to the essential elements of software engineering using the C programming language, tailored to those features that are used for developing C functions or modules for building a DSP library. The material associated with parts I, II and III is then used to build up a DSP system by defining a number of ‘problems’ and then addressing the solutions in terms of presenting an appropriate mathematical model, undertaking the necessary analysis, developing an appropriate algorithm and then coding the solution in C. This material forms the basis for part IV of this work. In most chapters, a series of tutorial problems is given for the reader to attempt with answers provided in Appendix A. These problems include theoretical, computational and programming exercises. Part II of this work is relatively long and arguably contains too much material on the computational methods for linear algebra. However, this material and the complementary material on vector and matrix norms forms the computational basis for many methods of digital signal processing. Moreover, this important and widely researched subject area forms the foundations, not only of digital signal processing and control engineering for example, but also of numerical analysis in general. The material presented in this book is based on the lecture notes and supplementary material developed by the author for an advanced Masters course ‘Digital Signal Processing’ which was first established at Cranfield University, Bedford in 1990 and modified when the author moved to De Montfort University, Leicester in 1994. The programmes are still operating at these universities and the material has been used by some 700++ graduates since its establishment and development in the early 1990s. The material was enhanced and developed further when the author moved to the Department of Electronic and Electrical Engineering at Loughborough University in 2003 and now forms part of the Department’s post-graduate programmes in Communication Systems Engineering. The original Masters programme included a taught component covering a period of six months based on two semesters, each Semester being composed of four modules. The material in this work covers the first Semester and its four parts reflect the four modules delivered. The material delivered in the second Semester is published as a companion volume to this work entitled Digital Image Processing, Horwood Publishing, 2005 which covers the mathematical modelling of imaging systems and the techniques that have been developed to process and analyse the data such systems provide. Since the publication of the first edition of this work in 2003, a number of minor changes and some additions have been made. The material on programming and software engineering in Chapters 11 and 12 has been extended. This includes some additions and further solved and supplementary questions which are included throughout the text. Nevertheless, it is worth pointing out, that while every effort has been made by the author and publisher to provide a work that is error free, it is inevitable that typing errors and various ‘bugs’ will occur. If so, and in particular, if the reader starts to suffer from a lack of comprehension over certain aspects of the material (due to errors or otherwise) then he/she should not assume that there is something wrong with themselves, but with the author

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

Assembling life : models, the cell, and the reformations of biological science, 1920-1960

Imperial Users onl

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement