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Cubic Dynamical Systems Vol X
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Book Synopsis Cubic Dynamical Systems, Vol. X by : Albert C. J. Luo
Download or read book Cubic Dynamical Systems, Vol. X written by Albert C. J. Luo and published by Springer. This book was released on 2024-06-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the tenth of 15 related monographs, discusses product-cubic nonlinear systems with two crossing-linear and self-quadratic products vector fields and the dynamic behaviors and singularity are presented through the first integral manifolds. The equilibrium and flow singularity and bifurcations discussed in this volume are for the appearing and switching bifurcations. The double-saddle equilibriums described are the appearing bifurcations for saddle source and saddle-sink, and for a network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations are also presented, specifically: · Inflection-saddle infinite-equilibriums, · Hyperbolic (hyperbolic-secant)-sink and source infinite-equilibriums · Up-down and down-up saddle infinite-equilibriums, · Inflection-source (sink) infinite-equilibriums.
Book Synopsis Cubic Dynamical Systems, Vol VIII by : Albert C. J. Luo
Download or read book Cubic Dynamical Systems, Vol VIII written by Albert C. J. Luo and published by Springer. This book was released on 2024-09-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the eighth of 15 related monographs, discusses a product-cubic dynamical system possessing a product-cubic vector field and a crossing-univariate quadratic vector field. It presents equilibrium singularity and bifurcation dynamics, and . the saddle-source (sink) examined is the appearing bifurcations for saddle and source (sink). The double-inflection saddle equilibriums are the appearing bifurcations of the saddle and center, and also the appearing bifurcations of the network of saddles and centers. The infinite-equilibriums for the switching bifurcations featured in this volume include: Parabola-source (sink) infinite-equilibriums, Inflection-source (sink) infinite-equilibriums, Hyperbolic (circular) sink-to source infinite-equilibriums, Hyperbolic (circular) lower-to-upper saddle infinite-equilibriums.
Book Synopsis Cubic Dynamical Systems, Vol. V by : Albert C. J. Luo
Download or read book Cubic Dynamical Systems, Vol. V written by Albert C. J. Luo and published by Springer. This book was released on 2024-05-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center. Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations.
Book Synopsis Dynamical Systems by : Rafael Labarca
Download or read book Dynamical Systems written by Rafael Labarca and published by CRC Press. This book was released on 1993-02-22 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: In at least five countries in Latin America, high level research in the field in taking place. To stimulate this development both at home and abroad, Chilean mathematicians have been promoting international meetings like the III International School of Dynamical Systems, which took place at the Universidad de Santiago de Chile-Santiago in 1990. A number of distinguished mathematicians were present at the meeting, side by side with younger people interested in the subject. Several of the participants submitted original contributions to these proceedings of the school. The topics of the papers are central to dynamics: ergodic theory, real and complex foliations, fractal dimensions, polynomial vector fields, hyperbolicity, and expansive maps. Notes on the ergodic theory of plane billiards are also included. This book will be of particular interest to researchers and graduate students working in mathematics, particularly in ordinary differential equations, bifurcation theory, and dynamical systems. Also those working in mathematical physics and physics.
Book Synopsis Dynamical Systems by : I?Akov Grigor?evich Sina?
Download or read book Dynamical Systems written by I?Akov Grigor?evich Sina? and published by World Scientific. This book was released on 1991 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.
Book Synopsis Two-Dimensional Two-Product Cubic Systems, Vol. X by : Albert C. J. Luo
Download or read book Two-Dimensional Two-Product Cubic Systems, Vol. X written by Albert C. J. Luo and published by Springer Nature. This book was released on with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Dynamical Systems by : H. Broer
Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Book Synopsis State Estimation for Dynamic Systems by : Felix L. Chernousko
Download or read book State Estimation for Dynamic Systems written by Felix L. Chernousko and published by CRC Press. This book was released on 1993-11-09 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: State Estimation for Dynamic Systems presents the state of the art in this field and discusses a new method of state estimation. The method makes it possible to obtain optimal two-sided ellipsoidal bounds for reachable sets of linear and nonlinear control systems with discrete and continuous time. The practical stability of dynamic systems subjected to disturbances can be analyzed, and two-sided estimates in optimal control and differential games can be obtained. The method described in the book also permits guaranteed state estimation (filtering) for dynamic systems in the presence of external disturbances and observation errors. Numerical algorithms for state estimation and optimal control, as well as a number of applications and examples, are presented. The book will be an excellent reference for researchers and engineers working in applied mathematics, control theory, and system analysis. It will also appeal to pure and applied mathematicians, control engineers, and computer programmers.
Book Synopsis Two-dimensional Self and Product Cubic Systems, Vol. II by : Albert C. J. Luo
Download or read book Two-dimensional Self and Product Cubic Systems, Vol. II written by Albert C. J. Luo and published by Springer. This book was released on 2024-05-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).
Book Synopsis Differential Equations: A Dynamical Systems Approach by : John H. Hubbard
Download or read book Differential Equations: A Dynamical Systems Approach written by John H. Hubbard and published by Springer Science & Business Media. This book was released on 1991 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a continuation of the subject matter discussed in the first book, with an emphasis on systems of ordinary differential equations and will be most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as in the life sciences, physics, and economics. After an introduction, there follow chapters on systems of differential equations, of linear differential equations, and of nonlinear differential equations. The book continues with structural stability, bifurcations, and an appendix on linear algebra. The whole is rounded off with an appendix containing important theorems from parts I and II, as well as answers to selected problems.
Book Synopsis Dynamic Systems Models by : Josif A. Boguslavskiy
Download or read book Dynamic Systems Models written by Josif A. Boguslavskiy and published by Springer. This book was released on 2016-03-22 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.
Book Synopsis Two-dimensional Product Cubic Systems, Vol. VII by : Albert C. J. Luo
Download or read book Two-dimensional Product Cubic Systems, Vol. VII written by Albert C. J. Luo and published by Springer. This book was released on 2024-06-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include: • inflection-saddle infinite-equilibriums, • hyperbolic-source (sink) infinite-equilibriums, • up-down (down-up) saddle infinite-equilibriums, • inflection-source (sink) infinite-equilibriums.
Book Synopsis The Arithmetic of Dynamical Systems by : J.H. Silverman
Download or read book The Arithmetic of Dynamical Systems written by J.H. Silverman and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
Book Synopsis Handbook of Dynamic System Modeling by : Paul A. Fishwick
Download or read book Handbook of Dynamic System Modeling written by Paul A. Fishwick and published by CRC Press. This book was released on 2007-06-01 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic Sy
Book Synopsis Equidistribution Of Dynamical Systems: Time-quantitative Second Law by : Jozsef Beck
Download or read book Equidistribution Of Dynamical Systems: Time-quantitative Second Law written by Jozsef Beck and published by World Scientific. This book was released on 2020-10-05 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: We know very little about the time-evolution of many-particle dynamical systems, the subject of our book. Even the 3-body problem has no explicit solution (we cannot solve the corresponding system of differential equations, and computer simulation indicates hopelessly chaotic behaviour). For example, what can we say about the typical time evolution of a large system starting from a stage far from equilibrium? What happens in a realistic time scale? The reader's first reaction is probably: What about the famous Second Law (of thermodynamics)?Unfortunately, there are plenty of notorious mathematical problems surrounding the Second Law. (1) How to rigorously define entropy? How to convert the well known intuitions (like 'disorder' and 'energy spreading') into precise mathematical definitions? (2) How to express the Second Law in forms of a rigorous mathematical theorem? (3) The Second Law is a 'soft' qualitative statement about entropy increase, but does not say anything about the necessary time to reach equilibrium.The object of this book is to answer questions (1)-(2)-(3). We rigorously prove a Time-Quantitative Second Law that works on a realistic time scale. As a by product, we clarify the Loschmidt-paradox and the related reversibility/irreversibility paradox.
Book Synopsis Proceedings Of The 4th Experimental Chaos Conference by : William L Ditto
Download or read book Proceedings Of The 4th Experimental Chaos Conference written by William L Ditto and published by World Scientific. This book was released on 1998-12-01 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 4th Experimental Chaos Conference was a forum for members of the scientific and engineering communities to discuss recent developments in, and techniques of, experimental nonlinear dynamics. The focus of this important conference was on actual realizations of nonlinear and chaotic systems. The latest developments in applications of nonlinear dynamics and chaos were presented, the requirement being that all presentations were actually implemented in experiments or devices. The areas covered were spatio-temporal patterns, optical chaos, biological dynamics, communication and synchronization, control of chaotic systems, mechanical dynamics, fluid dynamics, quantum chaos, and chaotic condensed matter systems.
Book Synopsis Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles by : Maoan Han
Download or read book Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles written by Maoan Han and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
