Polynomial Functional Dynamical Systems
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Polynomial Functional Dynamical Systems
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Author : Albert Luo
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Polynomial Functional Dynamical Systems written by Albert Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
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.
Polynomial Functional Dynamical Systems
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Author : Albert C. J. Luo
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2021-09-10
Polynomial Functional Dynamical Systems written by Albert C. J. Luo and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-10 with Technology & Engineering categories.
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 (2l + 1)th-order sink and source switching bifurcations for (2li)th-order saddles and (2lj +1)-order nodes are also presented, and the (2l)th-order upper-saddle and lower-saddle switching and appearing bifurcations are presented for (2li)th-order upper-saddles and (2lj)th-order lower-saddles (i, j = 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.
Polynomial And Rational Matrices
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Author : Tadeusz Kaczorek
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-19
Polynomial And Rational Matrices written by Tadeusz Kaczorek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-19 with Technology & Engineering categories.
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.
Stability Periodicity And Boundedness In Functional Dynamical Systems On Time Scales
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Author : Murat Adıvar
language : en
Publisher: Springer Nature
Release Date : 2020-04-23
Stability Periodicity And Boundedness In Functional Dynamical Systems On Time Scales written by Murat Adıvar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Mathematics categories.
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.
Orthogonal Functions In Systems And Control
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Author : Kanti Bhushan Datta
language : en
Publisher: World Scientific
Release Date : 1995
Orthogonal Functions In Systems And Control written by Kanti Bhushan Datta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Modelling Of Simplified Dynamical Systems
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Author : Edward Layer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modelling Of Simplified Dynamical Systems written by Edward Layer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.
The Arithmetic Of Polynomial Dynamical Pairs
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Author : Charles Favre
language : en
Publisher: Princeton University Press
Release Date : 2022-06-14
The Arithmetic Of Polynomial Dynamical Pairs written by Charles Favre and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-14 with Mathematics categories.
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.
Oscillations In Planar Dynamic Systems
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 1996-01-11
Oscillations In Planar Dynamic Systems written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-11 with Mathematics categories.
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
Multi Resolution Methods For Modeling And Control Of Dynamical Systems
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Author : Puneet Singla
language : en
Publisher: CRC Press
Release Date : 2008-08-01
Multi Resolution Methods For Modeling And Control Of Dynamical Systems written by Puneet Singla and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-01 with Mathematics categories.
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
Continuous Time Dynamical Systems
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Author : B.M. Mohan
language : en
Publisher: CRC Press
Release Date : 2018-10-08
Continuous Time Dynamical Systems written by B.M. Mohan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Technology & Engineering categories.
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