Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations)
Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations)

Author: Junji Kato

Publisher: Routledge

Published: 2019-09-09

Total Pages: 280

ISBN-13: 1351414852

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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.

Dichotomies and Stability in Nonautonomous Linear Systems
Dichotomies and Stability in Nonautonomous Linear Systems

Author: Yu. A. Mitropolsky

Publisher: CRC Press

Published: 2002-10-10

Total Pages: 394

ISBN-13: 9780415272216

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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
Stability and Bifurcation Theory for Non-Autonomous Differential Equations

Author: Anna Capietto

Publisher: Springer

Published: 2012-12-14

Total Pages: 314

ISBN-13: 3642329063

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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
Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Author: Martin Rasmussen

Publisher: Springer Science & Business Media

Published: 2007-06-08

Total Pages: 222

ISBN-13: 3540712240

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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
Nonautonomous Dynamics

Author: David N. Cheban

Publisher: Springer Nature

Published: 2020-01-22

Total Pages: 449

ISBN-13: 3030342921

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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
Stability of Differential Equations with Aftereffect

Author: N.V. Azbelev

Publisher: CRC Press

Published: 2002-10-03

Total Pages: 246

ISBN-13: 9780415269575

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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
Asymptotic Methods in Resonance Analytical Dynamics

Author: Eugeniu Grebenikov

Publisher: CRC Press

Published: 2004-03-02

Total Pages: 282

ISBN-13: 9780203409831

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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.

Dynamical Systems and Control
Dynamical Systems and Control

Author: Firdaus E. Udwadia

Publisher: CRC Press

Published: 2004-05-10

Total Pages: 450

ISBN-13: 0203694589

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The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniq

Stabilization of Programmed Motion
Stabilization of Programmed Motion

Author: E Ya Smirnov

Publisher: CRC Press

Published: 2000-09-20

Total Pages: 286

ISBN-13: 9789056992569

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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
Optimal Control of the Growth of Wealth of Nations

Author: E.N. Chukwu

Publisher: CRC Press

Published: 2003-01-23

Total Pages: 412

ISBN-13: 9780415269667

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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.