An Introduction to Sequential Dynamical Systems PDF Download

Author: Henning Mortveit
Publisher: Springer Science & Business Media
ISBN: 0387498796
Category : Mathematics
Languages : en
Pages : 261

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Book Description
This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Author: G.C. Layek
Publisher: Springer
ISBN: 8132225562
Category : Mathematics
Languages : en
Pages : 632

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Book Description
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Author: Michel Weber
Publisher: European Mathematical Society
ISBN: 9783037190463
Category : Mathematics
Languages : en
Pages : 778

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Book Description
This book presents in a concise and accessible way, as well as in a common setting, various tools and methods arising from spectral theory, ergodic theory and stochastic processes theory, which form the basis of and contribute interactively a great deal to the current research on almost-everywhere convergence problems. Researchers working in dynamical systems and at the crossroads of spectral theory, ergodic theory and stochastic processes will find the tools, methods, and results presented in this book of great interest. It is written in a style accessible to graduate students.

Author: Serban E. Vlad
Publisher: Elsevier
ISBN: 032395569X
Category : Mathematics
Languages : en
Pages : 458

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Book Description
The Boolean functions may be iterated either asynchronously, when their coordinates are computed independently of each other, or synchronously, when their coordinates are computed at the same time. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their use in modelling, author Serban E. Vlad presents a consistent and original mathematical theory of the discrete-time Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from the synchronous Boolean system theory and mostly from the synchronous real system theory, by analogy, and to indicate the way in which known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. The reader will be introduced to the dependence on the initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. A property of major importance is invariance, which is present in five versions. In relation to it, the reader will study the maximal invariant subsets, the minimal invariant supersets, the minimal invariant subsets, connectedness, separation, the basins of attraction, and attractors. The stability of the systems and their time-reversal symmetry end the topics that refer to the systems without input. The rest of the book is concerned with input systems. The most consistent chapters of this part of the book refer to the fundamental operating mode and to the combinational systems (systems without feedback). The chapter Wires, Gates, and Flip-Flops presents a variety of applications. The first appendix addresses the issue of continuous time, and the second one sketches the important theory of Daizhan Cheng, which is put in relation to asynchronicity. The third appendix is a bridge between asynchronicity and the symbolic dynamics of Douglas Lind and Brian Marcus. - Presents a consistent and original theory of the discrete-time Boolean asynchronous systems, which are useful for mathematicians and computer scientists interested in Boolean Networks, dynamical systems, and modeling. - Studies the flows and equations of evolution, nullclines, dependence on initial conditions, periodicity, path-connectedness, topological transitivity, chaos, nonwandering points, invariance, connectedness, and separation, as well as the basins of attraction, attractors, stability, and time-reversal symmetry. - Explains the fundamental operating mode of the input systems and the combinational systems (systems without feedback). - Includes a chapter of applications of the Boolean systems and their modeling techniques. - Makes use of the unbounded delay model of computation of the Boolean functions.

Author: Asish Ghosh
Publisher: Springer
ISBN: 3319107356
Category : Science
Languages : en
Pages : 252

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Book Description
This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.

Author: Olivier Bournez
Publisher: Springer
ISBN: 3642044204
Category : Computers
Languages : en
Pages : 243

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Book Description
This book constitutes the research papers presented at the 3rd International Workshop, RP 2009 held in Palaiseau, France, September 23-25, 2009. The 20 full papers of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures and predictability in iterative maps and new computational paradigms.

Author: Igor Potapov
Publisher: Springer Science & Business Media
ISBN: 3642044190
Category : Computers
Languages : en
Pages : 243

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Book Description
This book constitutes the research papers presented at the 3rd International Workshop, RP 2009 held in Palaiseau, France, September 23-25, 2009. The 20 full papers of this workshop reflect reachability problems that appear in algebraic structures, computational models, hybrid systems and verification. Reachability is a fundamental problem in the context of many models and abstractions which are describing various computational processes. Topics of interest include reachability problems in infinite state systems, rewriting systems, dynamical and hybrid systems, reachability problems in logic and verification, reachability analysis in different computational models, counter, timed, cellular, communicating automata, Petri-Nets, computational aspects of algebraic structures and predictability in iterative maps and new computational paradigms.

Author: Jiri Sgall
Publisher: Springer
ISBN: 3540446834
Category : Computers
Languages : en
Pages : 735

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Book Description
This book constitutes the refereed proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, MFCS 2001, held in Marianske Lazne, Czech Republic in August 2001. The 51 revised full papers presented together with 10 invited contributions were carefully reviewed and selected from a total of 118 submissions. All current aspects of theoretical computer science are addressed ranging from mathematical logic and programming theory to algorithms, discrete mathematics, and complexity theory. Besides classical issues, modern topics like quantum computing are discussed as well.

Author: Kenneth H. Rosen
Publisher: CRC Press
ISBN: 135164405X
Category : Mathematics
Languages : en
Pages : 1611

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Book Description
Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Author: Antonio M. Scarfone
Publisher: MDPI
ISBN: 3038974692
Category : Mathematics
Languages : en
Pages : 203

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Book Description
This book is a printed edition of the Special Issue "New Trends in Statistical Physics of Complex Systems" that was published in Entropy