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Polynomial Functional Dynamical Systems
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Book Synopsis Polynomial Functional Dynamical Systems by : Albert C J Luo
Download or read book Polynomial Functional Dynamical Systems written by Albert C J Luo and published by . This book was released on 2021-09-10 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2
Book Synopsis Polynomial Functional Dynamical Systems by : Albert Luo
Download or read book Polynomial Functional Dynamical Systems written by Albert Luo and published by Springer Nature. This book was released on 2022-05-31 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about the global stability and bifurcation of equilibriums in polynomial functional systems. Appearing and switching bifurcations of simple and higher-order equilibriums in the polynomial functional systems are discussed, and such bifurcations of equilibriums are not only for simple equilibriums but for higher-order equilibriums. The third-order sink and source bifurcations for simple equilibriums are presented in the polynomial functional systems. The third-order sink and source switching bifurcations for saddle and nodes are also presented, and the fourth-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for two second-order upper-saddles and two second-order lower-saddles, respectively. In general, the (2 + 1)th-order sink and source switching bifurcations for (2)th-order saddles and (2 +1)-order nodes are also presented, and the (2)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2)th-order upper-saddles and (2)th-order lower-saddles (, = 1,2,...). The vector fields in nonlinear dynamical systems are polynomial functional. Complex dynamical systems can be constructed with polynomial algebraic structures, and the corresponding singularity and motion complexity can be easily determined.
Book Synopsis Polynomial Functional Dynamical Systems$nAlbert C. J. Luo (Southern Illinois University, Edwardsville). by : Albert C. J. Luo
Download or read book Polynomial Functional Dynamical Systems$nAlbert C. J. Luo (Southern Illinois University, Edwardsville). written by Albert C. J. Luo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polynomial and Rational Matrices by : Tadeusz Kaczorek
Download or read book Polynomial and Rational Matrices written by Tadeusz Kaczorek and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. It provides the reader with rigorous and in-depth mathematical analysis of the uses of polynomial and rational matrices in the study of dynamical systems. It also throws new light on the problems of positive realization, minimum-energy control, reachability, and asymptotic and robust stability.
Book Synopsis Modelling of Simplified Dynamical Systems by : Edward Layer
Download or read book Modelling of Simplified Dynamical Systems written by Edward Layer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems involving synthesis of mathematical models of various physical systems, making use of these models in practice and verifying them qualitatively has - come an especially important area of research since more and more physical - periments are being replaced by computer simulations. Such simulations should make it possible to carry out a comprehensive analysis of the various properties of the system being modelled. Most importantly its dynamic properties can be - dressed in a situation where this would be difficult or even impossible to achieve through a direct physical experiment. To carry out a simulation of a real, phy- cally existing system it is necessary to have its mathematical description; the s- tem being described mathematically by equations, which include certain variables, their derivatives and integrals. If a single independent variable is sufficient in - der to describe the system, then derivatives and integrals with respect to only that variable will appear in the equations. Differentiation of the equation allows the integrals to be eliminated and produces an equation which includes derivatives with respect to only one independent variable i. e. an ordinary differential equation. In practice, most physical systems can be described with sufficient accuracy by linear differential equations with time invariant coefficients. Chapter 2 is devoted to the description of models by such equations, with time as the independent va- able.
Book Synopsis Planar Dynamical Systems by : Yirong Liu
Download or read book Planar Dynamical Systems written by Yirong Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago.Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Book Synopsis Orthogonal Functions in Systems and Control by : Kanti Bhushan Datta
Download or read book Orthogonal Functions in Systems and Control written by Kanti Bhushan Datta and published by World Scientific. This book was released on 1995 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This is the first book devoted to the application of orthogonal polynomials in systems and control, establishing the superiority of orthogonal polynomials to other orthogonal functions.
Book Synopsis The Arithmetic of Polynomial Dynamical Pairs by : Charles Favre
Download or read book The Arithmetic of Polynomial Dynamical Pairs written by Charles Favre and published by Princeton University Press. This book was released on 2022-06-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.
Book Synopsis Continuous Time Dynamical Systems by : B.M. Mohan
Download or read book Continuous Time Dynamical Systems written by B.M. Mohan and published by CRC Press. This book was released on 2018-10-08 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems
Book Synopsis Multi-Resolution Methods for Modeling and Control of Dynamical Systems by : Puneet Singla
Download or read book Multi-Resolution Methods for Modeling and Control of Dynamical Systems written by Puneet Singla and published by CRC Press. This book was released on 2008-08-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function
Book Synopsis An Introduction To Chaotic Dynamical Systems by : Robert Devaney
Download or read book An Introduction To Chaotic Dynamical Systems written by Robert Devaney and published by CRC Press. This book was released on 2018-03-09 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
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 Differential Geometry Applied to Dynamical Systems by : Jean-Marc Ginoux
Download or read book Differential Geometry Applied to Dynamical Systems written by Jean-Marc Ginoux and published by World Scientific. This book was released on 2009 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory OCo or the flow OCo may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Book Synopsis Seminar on Differential Equations and Dynamical Systems by : James A. Yorke
Download or read book Seminar on Differential Equations and Dynamical Systems written by James A. Yorke and published by Springer. This book was released on 2006-11-15 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics of Dynamical Systems by : H. H. Rosenbrock
Download or read book Mathematics of Dynamical Systems written by H. H. Rosenbrock and published by Wiley-Interscience. This book was released on 1970 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability Theory of Switched Dynamical Systems by : Zhendong Sun
Download or read book Stability Theory of Switched Dynamical Systems written by Zhendong Sun and published by Springer Science & Business Media. This book was released on 2011-01-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are plenty of challenging and interesting problems open for investigation in the field of switched systems. Stability issues help to generate many complex nonlinear dynamic behaviors within switched systems. The authors present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation, constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input. For each of these classes this book propounds: detailed stability analysis and/or design, related robustness and performance issues, connections to other control problems and many motivating and illustrative examples.
Download or read book Linear Dynamical Systems written by Casti and published by Academic Press. This book was released on 1987-03-19 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Dynamical Systems
