Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari 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 2012-12-06 with Mathematics categories.
In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Matthaeus Merian
language : en
Publisher:
Release Date : 1963
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Matthaeus Merian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Thomas Guy Hallam
language : en
Publisher:
Release Date : 1965
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Thomas Guy Hallam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : de
Publisher:
Release Date : 1959
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with categories.
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations
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Author : Harold Scott Macdonald Coxeter
language : en
Publisher:
Release Date : 1957
Asymptotic Behavior And Stability Problems In Ordinary Differential Equations written by Harold Scott Macdonald Coxeter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Differential equations categories.
Asymptotic Behaviour And Stability Problems In Ordinary Differential Equations
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Author : Lamberto Cesari
language : en
Publisher:
Release Date : 1971
Asymptotic Behaviour And Stability Problems In Ordinary Differential Equations written by Lamberto Cesari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Lecture Notes On Applied Analysis
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Author :
language : en
Publisher: World Scientific
Release Date : 2009
Lecture Notes On Applied Analysis written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Methods Of Bifurcation Theory
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Author : S.-N. Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Methods Of Bifurcation Theory written by S.-N. Chow 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 2012-12-06 with Mathematics categories.
An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.
Poincar Andronov Melnikov Analysis For Non Smooth Systems
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Author : Michal Feckan
language : en
Publisher: Academic Press
Release Date : 2016-06-07
Poincar Andronov Melnikov Analysis For Non Smooth Systems written by Michal Feckan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-07 with Mathematics categories.
Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity. - Extends Melnikov analysis of the classic Poincaré and Andronov staples, pointing to a general theory for freedom in dimensions of spatial variables and parameters as well as asymptotical results such as stability, instability, and hyperbolicity - Presents a toolbox of critical theoretical techniques for many practical examples and models, including non-smooth dynamical systems - Provides realistic models based on unsolved discontinuous problems from the literature and describes how Poincaré-Andronov-Melnikov analysis can be used to solve them - Investigates the relationship between non-smooth systems and their continuous approximations
Methods Of Nonlinear Analysis
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Author : Richard Bellman
language : en
Publisher: Elsevier
Release Date : 1970-04-01
Methods Of Nonlinear Analysis written by Richard Bellman and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970-04-01 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering