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Differential Equations With Impulse Effects
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Book Synopsis Differential Equations with Impulse Effects by : Nikolai A. Perestyuk
Download or read book Differential Equations with Impulse Effects written by Nikolai A. Perestyuk and published by Walter de Gruyter. This book was released on 2011-07-27 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.
Book Synopsis Theory of Impulsive Differential Equations by : V. Lakshmikantham
Download or read book Theory of Impulsive Differential Equations written by V. Lakshmikantham and published by World Scientific. This book was released on 1989 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Impulsive Differential Equations by : N Perestyuk
Download or read book Impulsive Differential Equations written by N Perestyuk and published by World Scientific. This book was released on 1995-08-31 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Impulsive Differential Equations with a Small Parameter by : Dimit?r Ba?nov
Download or read book Impulsive Differential Equations with a Small Parameter written by Dimit?r Ba?nov and published by World Scientific. This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.
Book Synopsis Impulsive Differential Equations by : Drumi Bainov
Download or read book Impulsive Differential Equations written by Drumi Bainov and published by Routledge. This book was released on 2017-11-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.
Book Synopsis Impulsive Differential Equations by : Drumi Bainov
Download or read book Impulsive Differential Equations written by Drumi Bainov and published by Routledge. This book was released on 2017-11-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.
Book Synopsis Stability Analysis of Impulsive Functional Differential Equations by : Ivanka Stamova
Download or read book Stability Analysis of Impulsive Functional Differential Equations written by Ivanka Stamova and published by Walter de Gruyter. This book was released on 2009-10-16 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Impulsive Differential Equations: Asymptotic Properties Of The Solutions by : Drumi D Bainov
Download or read book Impulsive Differential Equations: Asymptotic Properties Of The Solutions written by Drumi D Bainov and published by World Scientific. This book was released on 1995-03-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Book Synopsis Almost Periodic Solutions of Impulsive Differential Equations by : Gani T. Stamov
Download or read book Almost Periodic Solutions of Impulsive Differential Equations written by Gani T. Stamov and published by Springer. This book was released on 2012-03-08 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.
Book Synopsis State-Dependent Impulses by : Irena Rachůnková
Download or read book State-Dependent Impulses written by Irena Rachůnková and published by Springer. This book was released on 2015-09-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.
Book Synopsis Theory of Integro-Differential Equations by : V. Lakshmikantham
Download or read book Theory of Integro-Differential Equations written by V. Lakshmikantham and published by CRC Press. This book was released on 1995-03-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.
Book Synopsis Impulsive Differential Equations and Inclusions by : Mouffak Benchohra
Download or read book Impulsive Differential Equations and Inclusions written by Mouffak Benchohra and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Impulsive Differential Inclusions by : John R. Graef
Download or read book Impulsive Differential Inclusions written by John R. Graef and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Impulsive Differential Equations by : Dimit?r Ba?nov
Download or read book Impulsive Differential Equations written by Dimit?r Ba?nov and published by World Scientific. This book was released on 1995 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Book Synopsis Impulsive Differential Equations with Applications to Infectious Diseases by : Rachelle Miron
Download or read book Impulsive Differential Equations with Applications to Infectious Diseases written by Rachelle Miron and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Impulsive differential equations are useful for modelling certain biological events. We present three biological applications showing the use of impulsive differential equations in real-world problems. We also look at the effects of stability on a reduced two-dimensional impulsive HIV system. The first application is a system describing HIV induction-maintenance therapy, which shows how the solution to an impulsive system is used in order to find biological results (adherence, etc). A second application is an HIV system describing the interaction between T-cells, virus and drugs. Stability of the system is determined for a fixed drug level in three specific regions: low, intermediate and high drug levels. Numerical simulations show the effects of varying drug levels on the stability of a system by including an impulse. We reduce these two models to a two-dimensional impulsive model. We show analytically the existence and uniqueness of T-periodic solutions, and show how stability changes when varying the immune response rate, the impulses and a certain nonlinear infection term. The third application shows how seasonal changes can be incorporated into an impulsive differential system of Rift Valley Fever, and looks at how stability may differ when impulses are included. The analysis of impulsive differential systems is crucial in developing more realistic mathematical models for infectious diseases.
Book Synopsis Scaling of Differential Equations by : Hans Petter Langtangen
Download or read book Scaling of Differential Equations written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-15 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Book Synopsis Functional and Impulsive Differential Equations of Fractional Order by : Ivanka Stamova
Download or read book Functional and Impulsive Differential Equations of Fractional Order written by Ivanka Stamova and published by CRC Press. This book was released on 2017-03-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
