Stability Analysis Of Impulsive Functional Differential Equations
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Stability Analysis Of Impulsive Functional Differential Equations
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Author : Ivanka Stamova
language : en
Publisher: Walter de Gruyter
Release Date : 2009-10-16
Stability Analysis Of Impulsive Functional Differential Equations written by Ivanka Stamova and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-16 with Mathematics categories.
This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Functional And Impulsive Differential Equations Of Fractional Order
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Author : Ivanka Stamova
language : en
Publisher: CRC Press
Release Date : 2017-03-03
Functional And Impulsive Differential Equations Of Fractional Order written by Ivanka Stamova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-03 with Mathematics categories.
The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.
Stability Analysis Of Impulsive Functional Differential Equations
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Author : Ivanka Stamova
language : en
Publisher: Walter de Gruyter
Release Date : 2009
Stability Analysis Of Impulsive Functional Differential Equations written by Ivanka Stamova and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Impulsive Differential Inclusions
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Author : John R. Graef
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31
Impulsive Differential Inclusions written by John R. Graef and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.
Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.
Impulsive Differential Equations
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Author : A M Samoilenko
language : en
Publisher: World Scientific
Release Date : 1995-08-31
Impulsive Differential Equations written by A M Samoilenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-31 with Science categories.
Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts
Theory Of Impulsive Differential Equations
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Author : V. Lakshmikantham
language : en
Publisher: World Scientific
Release Date : 1989
Theory Of Impulsive Differential Equations written by V. Lakshmikantham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.
Impulsive Differential Equations And Inclusions
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Author : Mouffak Benchohra
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2006
Impulsive Differential Equations And Inclusions written by Mouffak Benchohra and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.
Applied Impulsive Mathematical Models
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Author : Ivanka Stamova
language : en
Publisher: Springer
Release Date : 2016-05-05
Applied Impulsive Mathematical Models written by Ivanka Stamova and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Science categories.
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Bifurcation Theory Of Impulsive Dynamical Systems
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Author : Kevin E.M. Church
language : en
Publisher: Springer Nature
Release Date : 2021-03-24
Bifurcation Theory Of Impulsive Dynamical Systems written by Kevin E.M. Church and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-24 with Mathematics categories.
This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
Advances In Stability Theory At The End Of The 20th Century
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Author : A.A. Martynyuk
language : en
Publisher: CRC Press
Release Date : 2002-10-03
Advances In Stability Theory At The End Of The 20th Century written by A.A. Martynyuk 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.
This volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first