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Author: Albert C J Luo
Publisher:
ISBN: 9781636392196
Category :
Languages : en
Pages : 166
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Book Description
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
Author: Albert C J Luo
Publisher:
ISBN: 9781636392196
Category :
Languages : en
Pages : 166
Get Book
Book Description
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
Author: Albert Luo
Publisher: Springer Nature
ISBN: 3031797094
Category : Technology & Engineering
Languages : en
Pages : 151
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Book Description
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.
Author: Tadeusz Kaczorek
Publisher: Springer Science & Business Media
ISBN: 1846286050
Category : Technology & Engineering
Languages : en
Pages : 514
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Book Description
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.
Author: Murat Adıvar
Publisher: Springer Nature
ISBN: 3030421171
Category : Mathematics
Languages : en
Pages : 416
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Book Description
Motivated by recent increased activity of research on time scales, the book provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales. Researchers and graduate students who are interested in the method of Lyapunov functions/functionals, in the study of boundedness of solutions, in the stability of the zero solution, or in the existence of periodic solutions should be able to use this book as a primary reference and as a resource of latest findings. This book contains many open problems and should be of great benefit to those who are pursuing research in dynamical systems or in Volterra integro-dynamic equations on time scales with or without delays. Great efforts were made to present rigorous and detailed proofs of theorems. The book should serve as an encyclopedia on the construction of Lyapunov functionals in analyzing solutions of dynamical systems on time scales. The book is suitable for a graduate course in the format of graduate seminars or as special topics course on dynamical systems. The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics and physics.
Author: Charles Favre
Publisher: Princeton University Press
ISBN: 0691235481
Category : Mathematics
Languages : en
Pages : 252
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Book Description
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.
Author: Yirong Liu
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110298368
Category : Mathematics
Languages : en
Pages : 389
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Book Description
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.
Author: Kanti Bhushan Datta
Publisher: World Scientific
ISBN: 9789810218898
Category : Mathematics
Languages : en
Pages : 296
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Book Description
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.
Author: Ronald E Mickens
Publisher: World Scientific
ISBN: 981450033X
Category : Mathematics
Languages : en
Pages : 340
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Book Description
This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples. Contents:Oscillatory SystemsLindstedt-Poincaré Perturbation MethodMethod of Krylov–Bogoliubov–MitropolskyHarmonic BalanceMulti-Time ExpansionsGeneral Second-Order SystemsAppendices Readership: Applied mathematicians. keywords:Nonlinear Oscillations;Perturbation Methods;Multi-Time Expansions;Harmonic Balance;Stability;Qualitative Theory of Differential Equations;Periodic Functions;Lindstedt-Poincare Method;Averaging Method “This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems … a clear presentation of necessary background materials and by the working out of many examples.” Lavoisier-Technique et Documentation
Author: Josif A. Boguslavskiy
Publisher: Springer
ISBN: 3319040367
Category : Science
Languages : en
Pages : 201
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Book Description
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.
Author: Puneet Singla
Publisher: CRC Press
ISBN: 1584887702
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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
