Download or read book Simulation and Sequential Dynamical Systems written by and published by . This book was released on 1999 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Sequential Dynamical Systems written by Henning Mortveit and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Sequential Dynamical Systems and Simulation written by and published by . This book was released on 1999 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Theoretical Issues of Computer Simulations Sequential Dynamical Systems written by and published by . This book was released on 1998 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study a class of discrete dynamical systems that is motivated by the generic structure of simulations. The systems consist of the following data: (a) a finite graph Y with vertex set {l_brace}1, ..., n{r_brace} where each vertex has a binary state, (b) functions F{sub i}:F2??20--?? → F2??20--?? and (c) an update ordering?. The functions F{sub i} update the binary state of vertex i as a function of the state of vertex i and its Y-neighbors and leave the states of all other vertices fixed. The update ordering is a permutation of the Y-vertices. They derive a decomposition result, characterize invertible SDS and study fixed points. In particular they analyze how many different SDS that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number. Finally, some specific SDS are investigated.
Download or read book Modeling Identification and Simulation of Dynamical Systems written by P. P. J. van den Bosch and published by CRC Press. This book was released on 2020-12-17 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Predecessor and Permutation Existence Problems for Sequential Dynamical Systems written by and published by . This book was released on 2002 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in BMR99, BR991 as a formal model for analyzing simulation systems. An SDS S is a triple (G, F, n), w here (i) G(V, E) is an undirected graph with n nodes with each node having a state, (ii) F = (fi, fi, . . ., fn), with fi denoting a function associated with node ui E V and (iii) A is a permutation of (or total order on) the nodes in V, A configuration of an SDS is an n-vector (b l, bz, . . ., bn), where bi is the value of the state of node vi. A single SDS transition from one configuration to another is obtained by updating the states of the nodes by evaluating the function associated with each of them in the order given by n. Here, we address the complexity of two basic problems and their generalizations for SDSs. Given an SDS S and a configuration C, the PREDECESSOR EXISTENCE (or PRE) problem is to determine whether there is a configuration C' such that S has a transition from C' to C. (If C has no predecessor, C is known as a garden of Eden configuration.) Our results provide separations between efficiently solvable and computationally intractable instances of the PRE problem. For example, we show that the PRE problem can be solved efficiently for SDSs with Boolean state values when the node functions are symmetric and the underlying graph is of bounded treewidth. In contrast, we show that allowing just one non-symmetric node function renders the problem NP-complete even when the underlying graph is a tree (which has a treewidth of 1). We also show that the PRE problem is efficiently solvable for SDSs whose state values are from a field and whose node functions are linear. Some of the polynomial algorithms also extend to the case where we want to find an ancestor configuration that precedes a given configuration by a logarithmic number of steps. Our results extend some of the earlier results by Sutner [Su95] and Green [@87] on the complexity of the PREDECESSOR EXISTENCE problem for 1-dimensional cellular automata. Given the underlying graph G(V, E), and two configurations C and C' of an SDS S, the PERMUTATION EXISTENCE (or PME) problem is to determine whether there is a permutation of nodes such that 8 has a transition from C' to C in one step. We show that the PME problem is NP-complete even when the function associated with each node is a simple-threshold function. We also show that a generalized version of the PME(GEN-PMEp)r oblem is NP-complete for SDSs where each node function is NOR and the underlying graph has a maximum node degree of 3. When each node computes the OR function or when each node computes the AND function, we show that the GEN-PMEpr oblem is solvable in polynomial time.
Download or read book FACTORIZATION OF SIMULATIONS written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discovering Dynamical Systems Through Experiment and Inquiry written by Thomas LoFaro and published by CRC Press. This book was released on 2021-03-22 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Dynamical Systems Through Experiment and Inquiry differs from most texts on dynamical systems by blending the use of computer simulations with inquiry-based learning (IBL). IBL is an excellent tool to move students from merely remembering the material to deeper understanding and analysis. This method relies on asking students questions first, rather than presenting the material in a lecture. Another unique feature of this book is the use of computer simulations. Students can discover examples and counterexamples through manipulations built into the software. These tools have long been used in the study of dynamical systems to visualize chaotic behavior. We refer to this unique approach to teaching mathematics as ECAP—Explore, Conjecture, Apply, and Prove. ECAP was developed to mimic the actual practice of mathematics in an effort to provide students with a more holistic mathematical experience. In general, each section begins with exercises guiding students through explorations of the featured concept and concludes with exercises that help the students formally prove the results. While symbolic dynamics is a standard topic in an undergraduate dynamics text, we have tried to emphasize it in a way that is more detailed and inclusive than is typically the case. Finally, we have chosen to include multiple sections on important ideas from analysis and topology independent from their application to dynamics.
Download or read book Analysis Problems for Sequential Dynamical Systems and Communicating State Machines written by and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simple sequential dynamical system (SDS) is a triple (G, F, [pi]), where (i) G(V, E) is an undirected graph with n nodes with each node having a 1-bit state, (ii) F = [f1, f2 ..., f{sub n}] is a set of local transition functions with f{sub i} denoting a Boolean function associated with node Vv{sub i} and (iii) [pi] is a fixed permutation of (i.e., a total order on) the nodes in V.A single SDS transition is obtained by updating the states of the nodes in V by evaluating the function associated with each of them in the order given by [pi]. Such a (finite) SDS is a mathematical abstraction of simulation systems [BMR99, BR99]. In this paper, we characterize the computational complexity of determining several phase space properties of SDSs. The properties considered are t-REACHABILITY ('Can a given SDS starting from configuration I reach configuration B in t or fewer transitions?'), REACHABILITY('Can a given SDS starting from configuration I ever reach configuration B?') and FIXED POINT REACHABILITY ('Can a given SDS starting from configuration I ever reach configuration in which it stays for ever?'). Our main result is a sharp dichotomy between classes of SDSs whose behavior is 'easy' to predict and those whose behavior is 'hard' to predict. Specifically, we show the following. (1) The t-REACHABILITY, REACHABILITY and the FIXED POINT REACHABILITY problems for SDSs are PSPACE-complete, even when restricted to graphs of bounded bandwidth (and hence of bounded pathwidth and treewidth) and when the function associated with each node is symmetric. The result holds even for regular graphs of constant degree where all the nodes compute the same symmetric Boolean function. (2) In contrast, the t-REACHABILITYm REACHABILITY and FIXED POINT REACHABILITY problems are solvable in polynomial time for SDSs when the Boolean function associated with each node is symmetric and monotone. Two important consequences of our results are the following: (i) The close correspondence between SDSs and cellular automata (CA), in conjunctio with our lower bounds for SDSs, yields stronger lower bounds on the complexity of reachability problems for CA than known previously. (ii) REACHABILITY problems for hierarchically-specified linearly inter-connected copies of a single finite automaton are EXPSPACE-hard. The results can be combined with our related results to show hardness of a number of equivalence relations for such automata. The results can also be used to demonstrate that determining the sensitivity to initial conditions of such automata (as proposed in [Mo90, BPT91]) is computationally intractable.
Download or read book Sequential dynamical systems written by Mariana Raykova and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling and Control of Discrete event Dynamic Systems written by Branislav Hrúz and published by Springer Science & Business Media. This book was released on 2007-08-17 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modelling and Simulation written by Louis G. Birta and published by Springer Science & Business Media. This book was released on 2007-10-14 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a balanced and integrated presentation of modelling and simulation activity for both Discrete Event Dynamic Systems (DEDS) and Continuous Time Dynamic Systems (CYDS). The authors establish a clear distinction between the activity of modelling and that of simulation, maintaining this distinction throughout. The text offers a novel project-oriented approach for developing the modelling and simulation methodology, providing a solid basis for demonstrating the dependency of model structure and granularity on project goals. Comprehensive presentation of the verification and validation activities within the modelling and simulation context is also shown.
Download or read book Ergodic Theory Analysis and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Download or read book Mathematical Modeling of Earth s Dynamical Systems written by Rudy Slingerland and published by Princeton University Press. This book was released on 2011-03-28 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html
Download or read book Unconventional Computation written by Cristian S. Calude and published by Springer Science & Business Media. This book was released on 2005-09-19 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Conference on Unconventional Computation, UC 2005, held in Sevilla, Spain in September 2005. The conference formerly was named Unconventional Models of Computation (UMC). The 19 revised full papers presented together with 5 invited full papers were carefully reviewed and selected for inclusion in the book. All major areas of unconventional computing models are covered in theory as well as in experiments and applications. Topics addressed are: natural computing including quantum, cellular, molecular, neural and evolutionary computing; chaos and dynamical systems based computing; and various proposals for computations that go beyond the Turing model.
Download or read book Simulation of Dynamic Systems with MATLAB and Simulink written by Harold Klee and published by CRC Press. This book was released on 2018-02-02 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous-system simulation is an increasingly important tool for optimizing the performance of real-world systems. The book presents an integrated treatment of continuous simulation with all the background and essential prerequisites in one setting. It features updated chapters and two new sections on Black Swan and the Stochastic Information Packet (SIP) and Stochastic Library Units with Relationships Preserved (SLURP) Standard. The new edition includes basic concepts, mathematical tools, and the common principles of various simulation models for different phenomena, as well as an abundance of case studies, real-world examples, homework problems, and equations to develop a practical understanding of concepts.
Download or read book Prospects for Simulation and Simulators of Dynamic Systems written by George Shapiro and published by . This book was released on 1967 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
