Analysis And Modelling Of Discrete Dynamical Systems
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| Author | : Ernesto Salinelli |
| Publisher | : Springer |
| Total Pages | : 398 |
| Release | : 2014-06-11 |
| Genre | : Mathematics |
| ISBN | : 3319022911 |
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economics. The exposition is self-contained: some appendices present prerequisites, algorithms and suggestions for computer simulations. The analysis of several examples is enriched by the proposition of many related exercises of increasing difficulty; in the last chapter the detailed solution is given for most of them.
| Author | : Branislav Hrúz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 342 |
| Release | : 2007-08-17 |
| Genre | : Science |
| ISBN | : 1846288770 |
Discrete-event dynamic systems (DEDs) permeate our world. They are of great importance in modern manufacturing processes, transportation and various forms of computer and communications networking. This book begins with the mathematical basics required for the study of DEDs and moves on to present various tools used in their modeling and control. Industrial examples illustrate the concepts and methods discussed, making this book an invaluable aid for students embarking on further courses in control, manufacturing engineering or computer studies.
| Author | : Daniel Benest |
| Publisher | : CRC Press |
| Total Pages | : 334 |
| Release | : 1998-10-28 |
| Genre | : Computers |
| ISBN | : 9789056996253 |
The theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration. Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles.
| Author | : Mohd Hafiz Mohd |
| Publisher | : Springer Nature |
| Total Pages | : 239 |
| Release | : 2019-10-11 |
| Genre | : Mathematics |
| ISBN | : 9813298324 |
This book is the result of Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.
| Author | : Calin Belta |
| Publisher | : Springer |
| Total Pages | : 291 |
| Release | : 2017-03-08 |
| Genre | : Technology & Engineering |
| ISBN | : 331950763X |
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
| 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 | : P. P. J. van den Bosch |
| Publisher | : CRC Press |
| Total Pages | : 212 |
| Release | : 2020-12-17 |
| Genre | : Mathematics |
| ISBN | : 0429605927 |
This book gives an in-depth introduction to the areas of modeling, identification, simulation, and optimization. These scientific topics play an increasingly dominant part in many engineering areas such as electrotechnology, mechanical engineering, aerospace, and physics. This book represents a unique and concise treatment of the mutual interactions among these topics. Techniques for solving general nonlinear optimization problems as they arise in identification and many synthesis and design methods are detailed. The main points in deriving mathematical models via prior knowledge concerning the physics describing a system are emphasized. Several chapters discuss the identification of black-box models. Simulation is introduced as a numerical tool for calculating time responses of almost any mathematical model. The last chapter covers optimization, a generally applicable tool for formulating and solving many engineering problems.
| Author | : Andrei Karatkevich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 171 |
| Release | : 2007-04-27 |
| Genre | : Technology & Engineering |
| ISBN | : 3540714642 |
Design of modern digital hardware systems and of complex software systems is almost always connected with parallelism. For example, execution of an object-oriented p- gram can be considered as parallel functioning of the co-operating objects; all modern operating systems are multitasking, and the software tends to be multithread; many complex calculation tasks are solved in distributed way. But designers of the control systems probably have to face parallelism in more evident and direct way. Controllers rarely deal with just one controlled object. Usually a system of several objects is to be controlled, and then the control algorithm naturally turns to be parallel. So, classical and very deeply investigated model of discrete device, Finite State Machine, is not expressive enough for the design of control devices and systems. Theoretically in most of cases behavior of a controller can be described by an FSM, but usually it is not convenient; such FSM description would be much more complex, than a parallel specification (even as a network of several communicating FSMs).
| Author | : Gabriel A. Wainer |
| Publisher | : CRC Press |
| Total Pages | : 520 |
| Release | : 2018-09-03 |
| Genre | : Technology & Engineering |
| ISBN | : 142007234X |
Collecting the work of the foremost scientists in the field, Discrete-Event Modeling and Simulation: Theory and Applications presents the state of the art in modeling discrete-event systems using the discrete-event system specification (DEVS) approach. It introduces the latest advances, recent extensions of formal techniques, and real-world examples of various applications. The book covers many topics that pertain to several layers of the modeling and simulation architecture. It discusses DEVS model development support and the interaction of DEVS with other methodologies. It describes different forms of simulation supported by DEVS, the use of real-time DEVS simulation, the relationship between DEVS and graph transformation, the influence of DEVS variants on simulation performance, and interoperability and composability with emphasis on DEVS standardization. The text also examines extensions to DEVS, new formalisms, and abstractions of DEVS models as well as the theory and analysis behind real-world system identification and control. To support the generation and search of optimal models of a system, a framework is developed based on the system entity structure and its transformation to DEVS simulation models. In addition, the book explores numerous interesting examples that illustrate the use of DEVS to build successful applications, including optical network-on-chip, construction/building design, process control, workflow systems, and environmental models. A one-stop resource on advances in DEVS theory, applications, and methodology, this volume offers a sampling of the best research in the area, a broad picture of the DEVS landscape, and trend-setting applications enabled by the DEVS approach. It provides the basis for future research discoveries and encourages the development of new applications.
| Author | : S. Engell |
| Publisher | : Springer |
| Total Pages | : 504 |
| Release | : 2002-07-10 |
| Genre | : Technology & Engineering |
| ISBN | : 3540438122 |
In 1995, the Deutsche Forschungsgemeinschaft (DFG), the largest public research funding organization in Germany, decided to launch a priority program (Schw- punktprogramm in German) calledKondisk– Dynamics and Control of Systems with Mixed Continuous and Discrete Dynamics. Such a priority program is usually sponsored for six years and supports about twenty scientists at a time, in engineering andcomputersciencemostlyyoungresearchersworkingforadoctoraldegree. There is a yearly competition across all disciplines of arts and sciences for the funding of such programs, and the group of proposers was the happy winner of a slot in that year. The program started in 1996 after an open call for proposals; the successful projects were presented and re-evaluated periodically, and new projects could be submitted simultaneously. During the course of the focused research program, 25 different projects were funded in 19 participating university institutes, some of the projects were collaborative efforts of two groups with different backgrounds, mostly one from engineering and one from computer science. There were two main motivations for establishingKondisk. The rst was the fact that technical systems nowadays are composed of physical components with (mostly) continuous dynamics and computerized control systems where the reaction to discrete events plays a major role, implemented in Programmable Logic Contr- lers (PLCs), Distributed Control Systems (DCSs) or real-time computer systems.
