Download or read book Probabilistic Properties of Deterministic Systems written by Andrzej Lasota and published by Cambridge University Press. This book was released on 2008-11-27 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Download or read book Statistical Properties of Deterministic Systems written by Jiu Ding and published by . This book was released on 2009 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Properties of Deterministic Systems written by Jiu Ding and published by Springer Science & Business Media. This book was released on 2010-06-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system. The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering. Dr. Jiu Ding is a professor at the Department of Mathematics of the University of Southern Mississippi; Dr. Aihui Zhou is a professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.
Download or read book Deterministic Nonlinear Systems written by Vadim S. Anishchenko and published by Springer. This book was released on 2014-06-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Download or read book Probability in Physics written by Yemima Ben-Menahem and published by Springer Science & Business Media. This book was released on 2012-01-25 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.
Download or read book Abstraction Refinement and Proof for Probabilistic Systems written by Annabelle McIver and published by Springer Science & Business Media. This book was released on 2005 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.
Download or read book Chaos Fractals and Noise written by Andrzej Lasota and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.
Download or read book Introduction to Probabilistic Automata written by Azaria Paz and published by Academic Press. This book was released on 2014-05-10 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Probabilistic Automata deals with stochastic sequential machines, Markov chains, events, languages, acceptors, and applications. The book describes mathematical models of stochastic sequential machines (SSMs), stochastic input-output relations, and their representation by SSMs. The text also investigates decision problems and minimization-of-states problems arising from concepts of equivalence and coverings for SSMs. The book presents the theory of nonhomogeneous Markov chains and systems in mathematical terms, particularly in relation to asymptotic behavior, composition (direct sum or product), and decomposition. "Word functions," induced by Markov chains and valued Markov systems, involve characterization, equivalence, and representability by an underlying Markov chain or system. The text also discusses the closure properties of probabilistic languages, events and their relation to regular events, particularly with reference to definite, quasidefinite, and exclusive events. Probabilistic automata theory has applications in information theory, control, learning theory, pattern recognition, and time sharing in computer programming. Programmers, computer engineers, computer instructors, and students of computer science will find the collection highly valuable.
Download or read book Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and published by World Scientific. This book was released on 2024-04-22 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Download or read book Stochastic Methods In Experimental Sciences written by Waclaw Kasprzak and published by World Scientific. This book was released on 1990-08-23 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, containing selected papers presented during the COSMEX '89 meeting, provides readers with integrative and innovative articles on many aspects on many aspects of stochastic methods and their applications to experimental sciences. Offering an interdisciplinary presentation on the uses of stochastic methods, this publication discusses the practical applications of stochastic methods to such diverse areas as biology, chemistry, physics, mechanics and engineering. It also discusses computer implementation of theoretically derived algorithms especially for experimental designs.
Download or read book General System Theory Perspectives in Philosophy and Approaches in Complex Systems written by Gianfranco Minati and published by MDPI. This book was released on 2018-07-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Second Generation General System Theory: Perspectives in Philosophy and Approaches in Complex Systems" that was published in Systems
Download or read book Topics in Nonlinear Dynamics written by Erik Mosekilde and published by World Scientific. This book was released on 1997-01-04 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science. Contents:Deterministic Approach to Die TossingBifurcation Analysis of Simple Nonlinear SystemsCoupled Period-Doubling SystemsChaos in Technical Control SystemsEcological and Microbiological Population DynamicsPhysiological Control SystemsChaos and Hyperchaos in Economic and Managerial SystemsSpatiotemporal Phenomena in Extended Systems Readership: Nonlinear scientists. keywords:
Download or read book Probability Towards 2000 written by L. Accardi and published by Springer Science & Business Media. This book was released on 1998-03-27 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.
Download or read book Stochastic Versus Deterministic Systems of Iterative Processes written by Gangaram S Ladde and published by . This book was released on 2024-06-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: State continuous dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend mode of convergence. Second, the basic probabilistic and statistical properties mean, variance, moments of qualitative/quantitative behaviour of solutions are directly described as concept of solution process or via probability distribution or density functions either. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focussed on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the problems outlined above and made slow progress in developing problems as a result. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Download or read book Stochastic versus Deterministic Systems of Differential Equations written by G. S. Ladde and published by CRC Press. This book was released on 2003-12-05 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its methodological backbone, Stochastic Versus Deterministic Systems of Differential Equations addresses questions relating to the need for a stochastic mathematical model and the between-model contrast that arises in the absence of random disturbances/fluctuations and parameter uncertainties both deterministic and stochastic.
Download or read book Patrick Suppes Scientific Philosopher written by P. Humphreys and published by Springer Science & Business Media. This book was released on 1994-09-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Patrick Suppes is a philosopher and scientist whose contributions range over probability and statistics, mathematical and experimental psychology, the foundations of physics, education theory, the philosophy of language, measurement theory, and the philosophy of science. He has also been a pioneer in the area of computer assisted instruction. In each of these areas, Suppes has provided seminal ideas that in some cases led to shaping the direction of research in the field. The papers contained in this collection were commissioned with the mandate of advancing research in their respective fields rather than retrospectively surveying the contributions that Suppes himself has made. The authors form an interesting mixture of researchers in both formal philosophy of science and science itself all of whom have been inspired by his ideas. To maintain the spirit of constructive dialogue that characterizes Suppes's intellectual style, he has written individual responses to each article. In Volume 1: Probability and Probabilistic Causality, nineteen distinguished philosophers and scientists focus their attention on probabilistic issues. In Part I the contributors explore axiomatic representations of probability theory including qualitative and interval valued probabilities as well as traditional point valued probabilities. Belief structures and the dynamics of belief are also treated in detail. In Part II the rapidly growing field of probabilistic causation is assessed from both formal and empirical viewpoints. For probability theorists, statisticians, economists, philosophers of science, psychologists and those interested in the foundations of mathematical social science. In Volume 2: Philosophy of Physics, Theory Structure, and Measurement Theory, fifteen distinguished philosophers and scientists cover a wide variety of topics. Part III covers issues in quantum theory, geometry, classical mechanics, and computational physics. Part IV explores Suppes's well known set-theoretic account of scientific theories which has served him well throughout his career. Suppes's contributions to measurement theory have been widely used in mathematical psychology and elsewhere, and this material is the subject of Part V. For physicists, logicians, workers in mathematical social sicence, and philosophers of science. In Volume 3: Philosophy of Language and Logic, Learning and Action Theory, fourteen distinguished philosophers and scientists explore issues in the philosophy of language, logic, and philosophical psychology. Suppes's suggestions that quantum theory requires a rethinking of classical logic form a particularly sharp account of that controversial thesis, and Part VI deals with this issue together with topics in the philosophy of language and logic, including relational grammars and anaphora. Part VII deals with issues in psychology, action theory, and robotics, while Part VIII concludes with a general survey of Suppes's views in the philosophy of science. A comprehensive chronological and topical bibliography of Suppes's writings is included in this volume. For philosophers of language, theoretical linguists, logicians, workers in mathematical social sciences, and philosophers of science.
Download or read book Probabilistic Systems Analysis written by Arthur M. Breipohl and published by . This book was released on 1970 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary probability; Engineering applications of probability; Random variables; Expected values; Distribution of functions of Random variables; Applications of Random variables to systems problems; Distributions from data; Estimation; Engineering decisions; Introduction to Random processes; Systems and Random signals.
