Discrete Dynamical Systems And Chaotic Machines
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| Author | : Jacques M. Bahi |
| Publisher | : CRC Press |
| Total Pages | : 236 |
| Release | : 2013-06-07 |
| Genre | : Computers |
| ISBN | : 1466554509 |
For computer scientists, especially those in the security field, the use of chaos has been limited to the computation of a small collection of famous but unsuitable maps that offer no explanation of why chaos is relevant in the considered contexts. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science. Covering both theoretical and practical aspects, the book presents: Key mathematical and physical ideas in chaos theory Computer science fundamentals, clearly establishing that chaos properties can be satisfied by finite state machines Concrete applications of chaotic machines in computer security, including pseudorandom number generators, hash functions, digital watermarking, and steganography Concrete applications of chaotic machines in wireless sensor networks, including secure data aggregation and video surveillance Until the authors’ recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book illustrates how chaos theory enables the study of computer security problems, such as steganalysis, that otherwise could not be tackled. It also explains how the theory reinforces existing cryptographically secure tools and schemes.
| Author | : Jacques Bahi |
| Publisher | : CRC Press |
| Total Pages | : 232 |
| Release | : 2013-06-07 |
| Genre | : Computers |
| ISBN | : 1466554517 |
Until the authors' recent research, the practical implementation of the mathematical theory of chaos on finite machines raised several issues. This self-contained book shows how to make finite machines, such as computers, neural networks, and wireless sensor networks, work chaotically as defined in a rigorous mathematical framework. Taking into account that these machines must interact in the real world, the authors share their research results on the behaviors of discrete dynamical systems and their use in computer science.
| Author | : Mario Martelli |
| Publisher | : John Wiley & Sons |
| Total Pages | : 347 |
| Release | : 2011-11-01 |
| Genre | : Mathematics |
| ISBN | : 1118031121 |
A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.
| Author | : Steven H. Strogatz |
| Publisher | : CRC Press |
| Total Pages | : 532 |
| Release | : 2018-05-04 |
| Genre | : Mathematics |
| ISBN | : 0429961111 |
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
| Author | : Jose M. Rodriguez |
| Publisher | : MDPI |
| Total Pages | : 340 |
| Release | : 2019-03-14 |
| Genre | : Mathematics |
| ISBN | : 303897658X |
This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of “Graph Theory”. Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view.
| Author | : James D. Meiss |
| Publisher | : SIAM |
| Total Pages | : 410 |
| Release | : 2017-01-24 |
| Genre | : Mathematics |
| ISBN | : 161197464X |
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
| Author | : Sandra Pinelas |
| Publisher | : Springer Nature |
| Total Pages | : 754 |
| Release | : 2020-10-21 |
| Genre | : Mathematics |
| ISBN | : 3030563235 |
This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.
| Author | : Aboul Ella Hassanien |
| Publisher | : Springer Nature |
| Total Pages | : 737 |
| Release | : 2020-05-25 |
| Genre | : Technology & Engineering |
| ISBN | : 9811533830 |
This book presents the refereed proceedings of the 5th International Conference on Advanced Machine Learning Technologies and Applications (AMLTA 2020), held at Manipal University Jaipur, India, on February 13 – 15, 2020, and organized in collaboration with the Scientific Research Group in Egypt (SRGE). The papers cover current research in machine learning, big data, Internet of Things, biomedical engineering, fuzzy logic and security, as well as intelligence swarms and optimization.
| Author | : Qianxue Wang |
| Publisher | : Springer |
| Total Pages | : 118 |
| Release | : 2018-02-23 |
| Genre | : Technology & Engineering |
| ISBN | : 3319735497 |
This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework for composing them. The contributors demonstrate that the associated state networks of digital chaotic systems are strongly connected. They then further prove that digital chaotic systems satisfy Devaney’s definition of chaos on the domain of finite precision. The book presents Lyapunov exponents, as well as implementations to show the potential application of digital chaotic systems in the real world; the authors also discuss the basic advantages and practical benefits of this approach. The authors explore the solutions to dynamic degradation (including short cycle length, decayed distribution and low linear complexity) by proposing novel modelling methods and hardware designs for two different one-dimensional chaotic systems, which satisfy Devaney’s definition of chaos. They then extend it to a higher-dimensional digital-domain chaotic system, which has been used in image-encryption technology. This ensures readers do not encounter large differences between actual and theoretical chaotic orbits through small errors. Digital Chaotic Systems serves as an up-to-date reference on an important research topic for researchers and students in control science and engineering, computing, mathematics and other related fields of study.
| Author | : Robert Devaney |
| Publisher | : CRC Press |
| Total Pages | : 280 |
| Release | : 2018-03-09 |
| Genre | : Mathematics |
| ISBN | : 0429981937 |
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
