Stability Of Motion Of Nonautonomous Systems Methods Of Limiting Equations
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Stability Of Motion Of Nonautonomous Systems Methods Of Limiting Equations
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Author : Junji Kato
language : en
Publisher: Routledge
Release Date : 2019-09-09
Stability Of Motion Of Nonautonomous Systems Methods Of Limiting Equations written by Junji Kato and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
Stability Of Motion Of Nonautonomous Systems
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Author : Junji Kato
language : en
Publisher: CRC Press
Release Date : 2019-11-25
Stability Of Motion Of Nonautonomous Systems written by Junji Kato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with categories.
Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.
The Stability Of Dynamical Systems
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Author : J. P. LaSalle
language : en
Publisher: SIAM
Release Date : 1976-01-01
The Stability Of Dynamical Systems written by J. P. LaSalle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-01-01 with Difference equations categories.
An introduction to aspects of the theory of dynamial systems based on extensions of Liapunov's direct method. The main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations. The latest results on invariance properties for non-autonomous time-varying systems processes are presented for difference and differential equations.
Stability Of Nonautonomous Systems
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Author : J. P. LaSalle
language : en
Publisher:
Release Date : 1976
Stability Of Nonautonomous Systems written by J. P. LaSalle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Recent advances in the study of the limiting equations of nonautonomous systems and the invariance properties of positive limit sets of solutions motivate improving some of the known results connected with Liapunov's direct method. The report contains improvements of a theorem due originally to Yoshizawa and some improved sufficient conditions for asymptotic stability and instability. What is done is to again generalize the notion of a Liapunov function. It is noted how the new knowledge concerning invariance properties immediately sharpens the results.
Dichotomies And Stability In Nonautonomous Linear Systems
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Author : Yu. A. Mitropolsky
language : en
Publisher: CRC Press
Release Date : 2002-10-10
Dichotomies And Stability In Nonautonomous Linear Systems written by Yu. A. Mitropolsky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-10 with Mathematics categories.
Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms, to the solution of this problem. The authors explore the preservation of invariant tori of dynamic systems under perturbation. This volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.
Stability And Bifurcation Theory For Non Autonomous Differential Equations
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Author : Anna Capietto
language : en
Publisher: Springer
Release Date : 2012-12-14
Stability And Bifurcation Theory For Non Autonomous Differential Equations written by Anna Capietto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-14 with Mathematics categories.
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.
Attractivity And Bifurcation For Nonautonomous Dynamical Systems
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Author : Martin Rasmussen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-08
Attractivity And Bifurcation For Nonautonomous Dynamical Systems written by Martin Rasmussen 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 2007-06-08 with Mathematics categories.
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.
Nonautonomous Dynamics
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date : 2020-01-22
Nonautonomous Dynamics written by David N. Cheban and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Mathematics categories.
This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).
Stability Of Differential Equations With Aftereffect
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Author : N.V. Azbelev
language : en
Publisher: CRC Press
Release Date : 2002-10-03
Stability Of Differential Equations With Aftereffect written by N.V. Azbelev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-03 with Mathematics categories.
Stability of Differential Equations with Aftereffect presents stability theory for differential equations concentrating on functional differential equations with delay, integro-differential equations, and related topics. The authors provide background material on the modern theory of functional differential equations and introduce some new flexible methods for investigating the asymptotic behaviour of solutions to a range of equations. The treatment also includes some results from the authors' research group based at Perm and provides a useful reference text for graduates and researchers working in mathematical and engineering science.
Asymptotic Methods In Resonance Analytical Dynamics
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Author : Eugeniu Grebenikov
language : en
Publisher: CRC Press
Release Date : 2004-03-02
Asymptotic Methods In Resonance Analytical Dynamics written by Eugeniu Grebenikov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-02 with Mathematics categories.
Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.