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Author: Andrzej Lasota Publisher: Cambridge University Press ISBN: 9780521090964 Category : Mathematics Languages : en Pages : 376
Book Description
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.
Author: Andrzej Lasota Publisher: Cambridge University Press ISBN: 9780521090964 Category : Mathematics Languages : en Pages : 376
Book Description
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.
Author: Jiu Ding Publisher: Springer Science & Business Media ISBN: 3540853677 Category : Mathematics Languages : en Pages : 248
Book Description
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.
Author: Andrzej Lasota Publisher: Springer Science & Business Media ISBN: 146124286X Category : Mathematics Languages : en Pages : 481
Book Description
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.
Author: Vadim S. Anishchenko Publisher: Springer ISBN: 3319068717 Category : Science Languages : en Pages : 300
Book Description
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.
Author: Christos G. Cassandras Publisher: CRC Press ISBN: 1420008544 Category : Technology & Engineering Languages : en Pages : 301
Book Description
Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.
Author: P.S. Thiagarajan Publisher: Springer ISBN: 9783540606925 Category : Computers Languages : en Pages : 523
Book Description
This book constitutes the refereed proceedings of the 15th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS '95, held in Bangalore, India in December 1995. The volume presents 31 full revised research papers selected from a total of 106 submissions together with full papers of four invited talks. Among the topics covered are algorithms, software technology, functional programming theory, distributed algorithms, term rewriting and constraint logic programming, complexity theory, process algebras, computational geometry, and temporal logics and verification theory.
Author: Annabelle McIver Publisher: Springer Science & Business Media ISBN: 9780387401157 Category : Computers Languages : en Pages : 412
Book Description
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.
Author: Pijush Samui Publisher: Butterworth-Heinemann ISBN: 0128165464 Category : Computers Languages : en Pages : 592
Book Description
Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. - Explains the application of advanced probabilistic models encompassing multidisciplinary research - Applies probabilistic modeling to emerging areas in engineering - Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems
Author: Kuklev E.A. Publisher: Springer ISBN: 9811381224 Category : Technology & Engineering Languages : en Pages : 186
Book Description
This book provides a solution to “rare event” problems without using the classical theory of reliability and theory of probability. This solution is based on the methodology of risk assessment as “measure of danger” (in keeping with the ICS RAS) and an expert approach to determining systems’ safety indications using Fuzzy Sets methods. Further, the book puts forward a new concept: “Reliability, Risks, and Safety” (RRS). The book’s main goal is to generalize present results and underscore the need to develop an alternative approach to safety level assessment and risk management for technical (aviation) systems in terms of Fuzzy Sets objects, in addition to traditional probabilistic safety analysis (PSA). The concept it proposes incorporates ICAO recommendations regarding proactive system control and the system’s responses to various internal and external disturbances.
Author: Andrzej Lasota
Author: Andrzej Lasota
Author: Jiu Ding
Author: Andrzej Lasota
Author: Vadim S. Anishchenko
Author: Christos G. Cassandras
Author: P.S. Thiagarajan
Author: Annabelle McIver
Author: Pijush Samui
Author: Kuklev E.A.
Author: S. Ciliberto