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 arepresented 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:
Release Date : 2021-09-10
Polynomial Functional Dynamical Systems written by Albert C J Luo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-10 with 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
Dynamic Systems Models
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Author : Josif A. Boguslavskiy
language : en
Publisher: Springer
Release Date : 2016-03-22
Dynamic Systems Models written by Josif A. Boguslavskiy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Science categories.
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.
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.
Data Driven Methods For Dynamic Systems
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Author : Jason Bramburger
language : en
Publisher: SIAM
Release Date : 2024-11-05
Data Driven Methods For Dynamic Systems written by Jason Bramburger and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Science categories.
As experimental data sets have grown and computational power has increased, new tools have been developed that have the power to model new systems and fundamentally alter how current systems are analyzed. This book brings together modern computational tools to provide an accurate understanding of dynamic data. The techniques build on pencil-and-paper mathematical techniques that go back decades and sometimes even centuries. The result is an introduction to state-of-the-art methods that complement, rather than replace, traditional analysis of time-dependent systems. Data-Driven Methods for Dynamic Systems provides readers with methods not found in other texts as well as novel ones developed just for this book; an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities; and examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application. The online supplementary material includes a code repository that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book. This book is intended as an introduction to the field of data-driven methods for graduate students. It will also be of interest to researchers who want to familiarize themselves with the discipline. It can be used in courses on dynamical systems, differential equations, and data science.
Dynamical Systems
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Author : José A. Tenreiro Machado
language : en
Publisher: MDPI
Release Date : 2018-10-09
Dynamical Systems written by José A. Tenreiro Machado and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-09 with Science categories.
Printed Edition of the Special Issue Published in Entropy
Analysis And Control Of Polynomial Dynamic Models With Biological Applications
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Author : Gabor Szederkenyi
language : en
Publisher: Academic Press
Release Date : 2018-03-30
Analysis And Control Of Polynomial Dynamic Models With Biological Applications written by Gabor Szederkenyi and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-30 with Mathematics categories.
Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems. - Describes and illustrates the relationship between the dynamical, algebraic and structural features of the quasi-polynomial (QP) and kinetic models - Shows the applicability of kinetic and QP representation in biological modeling and control through examples and case studies - Emphasizes the importance and applicability of quantitative models in understanding and influencing natural phenomena
Dynamical Systems
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Author : Zeraoulia Elhadj
language : en
Publisher: CRC Press
Release Date : 2019-01-21
Dynamical Systems written by Zeraoulia Elhadj and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
Chaos is the idea that a system will produce very different long-term behaviors when the initial conditions are perturbed only slightly. Chaos is used for novel, time- or energy-critical interdisciplinary applications. Examples include high-performance circuits and devices, liquid mixing, chemical reactions, biological systems, crisis management, secure information processing, and critical decision-making in politics, economics, as well as military applications, etc. This book presents the latest investigations in the theory of chaotic systems and their dynamics. The book covers some theoretical aspects of the subject arising in the study of both discrete and continuous-time chaotic dynamical systems. This book presents the state-of-the-art of the more advanced studies of chaotic dynamical systems.
Polynomial Automorphisms
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Author : Arnoldus Richardus Petrus van den Essen
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Polynomial Automorphisms written by Arnoldus Richardus Petrus van den Essen 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 2000 with Automorphisms categories.
Control And Dynamic Systems V54 System Performance Improvement And Optimization Techniques And Their Applications In Aerospace Systems
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Author : C.T. Leonides
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Control And Dynamic Systems V54 System Performance Improvement And Optimization Techniques And Their Applications In Aerospace Systems written by C.T. Leonides and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Technology & Engineering categories.
Control and Dynamic Systems: Advances in Theory and Applications, Volume 54: System Performance Improvement and Optimization Techniques and their Applications in Aerospace Systems covers the issue of aerospace system performance and optimization techniques in aerospace systems. This book is composed of 12 chapters and begins with an examination of the techniques for aircraft conceptual design for mission performance. The succeeding chapters describe the balances and optimized design for aircraft and spacecraft structures through finite element procedures and the application of the knowledge-based system techniques for pilot aiding. These topics are followed by discussions of the optimal sensor placement for on-orbit modal identification experiments; the optimization techniques for helicopter airframe vibrations design; the size reduction techniques for efficient aeroservoelastic model determination; sensitivity analysis of eigendata of aeroelastic systems; and a simplified solution for transient structural dynamic problems with local nonlinearities. Other chapters explore a reduction algorithm for systems with integrators and the techniques for overcoming the difficulty of nonuniqueness of mode shape in modal analysis when random input data are not or cannot be measured. The last chapters consider the combined concepts of Krylov vectors and parameter matching and their application to develop model-reduction algorithms for structural dynamics. These chapters also provide the techniques for the development of new tracking algorithms that would incorporate explicit models of the maneuvering/nonmaneuvering phases of target encounter. This book will prove useful to aerospace, control, systems, and design engineers.