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Lyapunov Stability Of Non Autonomous Dynamical Systems
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Book Synopsis Stability of Nonautonomous Differential Equations by : Luis Barreira
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Book Synopsis Lyapunov Stability of Non-autonomous Dynamical Systems by : David N. Cheban
Download or read book Lyapunov Stability of Non-autonomous Dynamical Systems written by David N. Cheban and published by Nova Science Publishers. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The foundation of the modern theory of stability was created in the works of A Poincare and A M Lyapunov. The theory of the stability of motion has gained increasing significance in the last decade as is apparent from the large number of publications on the subject. A considerable part of these works are concerned with practical problems, especially problems from the area of controls and servo-mechanisms, and concrete problems from engineering, which first gave the decisive impetus for the expansion and modern development of stability theory. This book contains a systematic exposition of the elements of the asymptotic stability theory of general non-autonomous dynamical systems in metric spaces with an emphasis on the application for different classes of non-autonomous evolution equations (Ordinary Differential Equations (ODEs), Difference Equations (DEs), Functional-Differential Equations (FDEs), Semi-Linear Parabolic Equations etc). The basic results of this book are contained in the courses of lectures which the author has given during many years for the students of the State University of Moldova.This book is intended for mathematicians (scientists and university professors) who are working in the field of stability theory of differential/difference equations, dynamical systems and control theory. It would also be of use for the graduate and post graduate student who is interested in the theory of dynamical systems and its applications. The reader needs no deep knowledge of special branches of mathematics, although it should be easier for readers who know the fundamentals concepts of the theory of metric spaces, qualitative theory of differential/difference equations and dynamical systems.
Book Synopsis Nonlinear Systems Stability Analysis by : Seyed Kamaleddin Yadavar Nikravesh
Download or read book Nonlinear Systems Stability Analysis written by Seyed Kamaleddin Yadavar Nikravesh and published by CRC Press. This book was released on 2018-09-03 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value. Nonlinear Systems Stability Analysis: Lyapunov-Based Approach introduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems. Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.
Book Synopsis Random Dynamical Systems by : Ludwig Arnold
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Book Synopsis Nonautonomous Dynamical Systems by : Peter E. Kloeden
Download or read book Nonautonomous Dynamical Systems written by Peter E. Kloeden and published by American Mathematical Soc.. This book was released on 2011-08-17 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
Book Synopsis Nonuniform Hyperbolicity by : Luis Barreira
Download or read book Nonuniform Hyperbolicity written by Luis Barreira and published by . This book was released on 2014-02-19 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, comprehensive account of modern smooth ergodic theory, the mathematical foundation of deterministic chaos.
Book Synopsis Lyapunov Exponents and Smooth Ergodic Theory by : Luis Barreira
Download or read book Lyapunov Exponents and Smooth Ergodic Theory written by Luis Barreira and published by American Mathematical Soc.. This book was released on 2002 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to the core of smooth ergodic theory. An expanded version of an earlier work by the same authors, it describes the general (abstract) theory of Lyapunov exponents and the theory's applications to the stability theory of differential equations, the stable manifold theory, absolute continuity of stable manifolds, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). It could be used as a primary text for a course on nonuniform hyperbolic theory or as supplemental reading for a course on dynamical systems. Assumes a basic knowledge of real analysis, measure theory, differential equations, and topology. c. Book News Inc.
Book Synopsis Stability of Motion by : A. M. Liapunov
Download or read book Stability of Motion written by A. M. Liapunov and published by Elsevier. This book was released on 2016-06-03 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics in Science and Engineering, Volume 30: Stability of Motion deals with the problem of stability of motion. This volume investigates the problem of stability of the unperturbed motion in cases such as the system of differential equations for the perturbed motion is autonomie and the characteristic equation of the linear system that gives the first approximation has a double zero root. When the order of the system is larger than two (n > 2), all the remaining roots have negative real parts. The double root corresponds to a multiple elementary divisor of the characteristic matrix. This book is a good reference for mathematicians, students, and specialists conducting work on the stability of motion.
Book Synopsis Stability and Bifurcation Theory for Non-Autonomous Differential Equations by : Anna Capietto
Download or read book Stability and Bifurcation Theory for Non-Autonomous Differential Equations written by Anna Capietto and published by Springer. This book was released on 2012-12-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
Download or read book Dynamical Systems written by Werner Krabs and published by Springer Science & Business Media. This book was released on 2010-08-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.
Book Synopsis Finite-Time Stability: An Input-Output Approach by : Francesco Amato
Download or read book Finite-Time Stability: An Input-Output Approach written by Francesco Amato and published by John Wiley & Sons. This book was released on 2018-10-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
Book Synopsis Construction of Global Lyapunov Functions Using Radial Basis Functions by : Peter Giesl
Download or read book Construction of Global Lyapunov Functions Using Radial Basis Functions written by Peter Giesl and published by Springer. This book was released on 2007-04-11 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented in this volume intended for researchers and advanced students from both dynamical systems and radial basis functions. Besides an introduction to both areas and a detailed description of the method, it contains error estimates and many examples.
Book Synopsis General Problem of the Stability Of Motion by : A M Lyapunov
Download or read book General Problem of the Stability Of Motion written by A M Lyapunov and published by CRC Press. This book was released on 1992-08-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes more widely accessible the text of Lyapunov's major memoir of the general problem of the stability of motion. Translated by A. T. Fuller (University of Cambridge), the work is now available for the first time in the English language, and marked the centenary of the Russian publication in the late 1800s. Including a biography of Lyapunov and a comprehensive bibliography of his work, this excellent volume will prove to be of fundamental interest to all those concerned with the concept of the stability of motion, boundaries of stability, and with nonlinear dynamics.
Book Synopsis Lyapunov Functionals and Stability of Stochastic Functional Differential Equations by : Leonid Shaikhet
Download or read book Lyapunov Functionals and Stability of Stochastic Functional Differential Equations written by Leonid Shaikhet and published by Springer Science & Business Media. This book was released on 2013-03-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.
Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst
Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.
Book Synopsis An Introduction To Nonautonomous Dynamical Systems And Their Attractors by : Peter Kloeden
Download or read book An Introduction To Nonautonomous Dynamical Systems And Their Attractors written by Peter Kloeden and published by World Scientific. This book was released on 2020-11-25 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a 'Thousand Expert' Professorship at the Huazhong University of Science and Technology in Wuhan.
Book Synopsis Global Attractors of Non-autonomous Dissipative Dynamical Systems by : David N. Cheban
Download or read book Global Attractors of Non-autonomous Dissipative Dynamical Systems written by David N. Cheban and published by World Scientific. This book was released on 2004 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor.
