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Author: Irena Rachůnková
Publisher: Springer
ISBN: 9462391270
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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.
Author: Irena Rachůnková
Publisher: Springer
ISBN: 9462391270
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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.
Author: Irena Rachunková
Publisher:
ISBN: 9789462391284
Category :
Languages : en
Pages :
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Book Description
Author: Qing Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 204
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Book Description
The stability and boundedness theories are developed for impulsive differential equations with time delay. Definitions, notations and fundamental theory are presented for delay differential systems with both fixed and state-dependent impulses. It is usually more difficult to investigate the qualitative properties of systems with state-dependent impulses since different solutions have different moments of impulses. In this thesis, the stability problems of nontrivial solutions of systems with state-dependent impulses are ``transferred" to those of the trivial solution of systems with fixed impulses by constructing the so-called ``reduced system". Therefore, it is enough to investigate the stability problems of systems with fixed impulses. The exponential stability problem is then discussed for the system with fixed impulses. A variety of stability criteria are obtained and`numerical examples are worked out to illustrate the results, which shows that impulses do contribute to the stabilization of some delay differential equations. To unify various stability concepts and to offer a general framework for the investigation of stability theory, the concept of stability in terms of two measures is introduced and then several stability criteria are developed for impulsive delay differential equations by both the single and multiple Lyapunov functions method. Furthermore, boundedness and periodicity results are discussed for impulsive differential systems with time delay. The Lyapunov-Razumikhin technique, the Lyapunov functional method, differential inequalities, the method of variation of parameters, and the partitioned matrix method are the main tools to obtain these results. Finally, the application of the stability theory to neural networks is presented. In applications, the impulses are considered as either means of impulsive control or perturbations. Sufficient conditions for stability and stabilization of neural networks are obtained.
Author: Drumi Bainov
Publisher: Routledge
ISBN: 1351439103
Category : Mathematics
Languages : en
Pages : 238
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Book Description
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.
Author: N Perestyuk
Publisher: World Scientific
ISBN: 981449982X
Category : Science
Languages : en
Pages : 474
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Book Description
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
Author: Vangipuram Lakshmikantham
Publisher: World Scientific
ISBN: 9814507261
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
Author: Xiaodi Li
Publisher: Springer Nature
ISBN: 9811646872
Category : Technology & Engineering
Languages : en
Pages : 449
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Book Description
This book systematically presents the most recent progress in stability and control of impulsive systems with delays. Impulsive systems have recently attracted continued high research interests because they provide a natural framework for mathematical modeling of many real-world processes. It focuses not only on impulsive delayed systems, but also impulsive systems with delayed impulses and impulsive systems with event-triggered mechanism, including their Lyapunov stability, finite-time stability and input-to-state stability synthesis. Special attention is paid to the bilateral effects of the delayed impulses, where comprehensive stability properties are discussed in the framework of time-dependent and state-dependent delays. New original work with event-triggered impulsive control and its applications in multi-agent systems and collective dynamics are also provided. This book will be of use to specialists who are interested in the theory of impulsive differential equations and impulsive control theory, as well as high technology specialists who work in the fields of complex networks and applied mathematics. Also, instructors teaching graduate courses and graduate students will find this book a valuable source of nonlinear system theory.
Author: John R. Graef
Publisher: Walter de Gruyter
ISBN: 3110295318
Category : Mathematics
Languages : en
Pages : 412
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Book Description
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.
Author: Ivanka Stamova
Publisher: Walter de Gruyter
ISBN: 3110221829
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
Author: Remco I. Leine
Publisher: Springer Science & Business Media
ISBN: 3540769757
Category : Technology & Engineering
Languages : en
Pages : 241
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Book Description
While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.
