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 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 And Stabilization Of Nonlinear Systems With Random Structures
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Author : I. Ya Kats
language : en
Publisher: CRC Press
Release Date : 2002-08-22
Stability And Stabilization Of Nonlinear Systems With Random Structures written by I. Ya Kats and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-22 with Mathematics categories.
Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic systems with random Markov parameters. This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.
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
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.
Stabilization Of Programmed Motion
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Author : E Ya Smirnov
language : en
Publisher: CRC Press
Release Date : 2000-09-20
Stabilization Of Programmed Motion written by E Ya Smirnov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-20 with Mathematics categories.
This volume presents a particular aspect of control theory-stabilization of programmed motion. Methods of the construction and synthesis of stabilizing controls are introduced together with original results and useful examples. The problem of optimal stabilization control synthesis is solved for linear systems of difference equations with quadratic quality criterion.
Optimal Control Of The Growth Of Wealth Of Nations
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Author : E.N. Chukwu
language : en
Publisher: CRC Press
Release Date : 2003-01-23
Optimal Control Of The Growth Of Wealth Of Nations written by E.N. Chukwu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to "control" problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.
Volterra Equations And Applications
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Author : C. Corduneanu
language : en
Publisher: CRC Press
Release Date : 2000-01-10
Volterra Equations And Applications written by C. Corduneanu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-10 with Mathematics categories.
This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in the theory of integral equations and nonlinear functional analysis. Volterra series are of interest and use in pure and applied mathematics and engineering.