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| Author | : Norman MacDonald |
| Publisher | : Cambridge University Press |
| Total Pages | : 256 |
| Release | : 2008-01-03 |
| Genre | : Mathematics |
| ISBN | : 9780521048163 |
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for delays such as those due to gestation, maturation or transport. This book deals with a fundamental question in the analysis of the effects of delays, namely whether they affect the stability of steady states.
| Author | : Muthusamy Lakshmanan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 322 |
| Release | : 2011-01-04 |
| Genre | : Science |
| ISBN | : 3642149383 |
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.
| Author | : Tamás Insperger |
| Publisher | : Springer |
| Total Pages | : 359 |
| Release | : 2017-03-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3319534262 |
This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as well as experiments and case studies. The target audience primarily comprises research experts in the field of time delay systems, but the book may also be beneficial for graduate students alike.
| Author | : Silviu-Iulian Niculescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642184820 |
In the mathematical description of a physical or biological process, it is a common practice \0 assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho dology for analysis and control design for such systems, the lime-delay elements arc often either neglected or poorly approximated, which frequently results in analysis and simulation of insufficient accuracy, which in turns leads to poor performance of the systems designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriora ted perfonnances for the corresponding closed-loop systems.
| Author | : Patrick W Nelson |
| Publisher | : World Scientific |
| Total Pages | : 153 |
| Release | : 2010-06-25 |
| Genre | : Technology & Engineering |
| ISBN | : 9814464880 |
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays can cause problems (e.g. instability) and limit the achievable performance of control systems. The concise and self-contained volume uses the Lambert W function to obtain solutions to time-delay systems represented by delay differential equations. Subsequently, the solutions are used to analyze essential system properties and to design controllers precisely and effectively.
| Author | : Fathalla A. Rihan |
| Publisher | : Springer Nature |
| Total Pages | : 292 |
| Release | : 2021-08-19 |
| Genre | : Mathematics |
| ISBN | : 9811606269 |
This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.
| Author | : Magdi S. Mahmoud |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2018 |
| Genre | : Automatic control |
| ISBN | : 9781536130881 |
Time-delay occurs in many physical, industrial and engineering systems such as biological systems, chemical systems, metallurgical processing systems, nuclear reactors, hydraulic systems and electrical networks, to name a few. The reason for the occurrence could be attributed to inherent physical phenomena like mass transport flow or recycling. It could result from the finite capabilities of information processing and data transmission among various parts of the system. In addition, they could be by-products of computational delays or could be intentionally introduced for some design consideration. Such delays could be constant or time varying, known or unknown, deterministic or stochastic depending on the system under consideration. In recent years, time-delay, which exists in networked control systems, has brought more complex problems into a new research area. Frequently, it is a source of the generation of oscillation, instability and poor performance. Therefore, the subject of Time-Delay Systems (TDS) has been investigated as functional differential equations over the past four decades. Because the presence of the delay factor renders the system analysis more complicated, the problems of stability and stabilization are of great importance. This book presents some basic theories of stability and stabilization of systems with time-delays. More attention is paid to the synthesis of systems with time-delay. That is, control of nonlinear systems with delay; networked control systems; positive delay systems; fuzzy systems; and reset control with random delay are all analysed within this book.
| Author | : Yuanqing Xia |
| Publisher | : Springer |
| Total Pages | : 288 |
| Release | : 2009-10-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642026966 |
Time-delay occurs in many dynamical systems such as biological systems, chemical systems, metallurgical processing systems, nuclear reactor, long transmission lines in pneumatic, hydraulic systems and electrical networks. Especially, in recent years, time-delay which exists in networked control s- temshasbroughtmorecomplexproblemintoanewresearcharea.Frequently, itisasourceofthegenerationofoscillation,instabilityandpoorperformance. Considerable e?ort has been applied to di?erent aspects of linear time-delay systems during recent years. Because the introduction of the delay factor renders the system analysis more complicated, in addition to the di?culties caused by the perturbation or uncertainties, in the control of time-delay s- tems, the problems of robust stability and robust stabilization are of great importance. This book presents some basic theories of stability and stabilization of systems with time-delay, which are related to the main results in this book. More attention will be paid on synthesis of systems with time-delay. That is, sliding mode control of systems with time-delay; networked control systems with time-delay; networked data fusion with random delay.
| Author | : N. MacDonald |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 122 |
| Release | : 2013-03-08 |
| Genre | : Mathematics |
| ISBN | : 3642931073 |
In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms.
| Author | : Daniel B. Forger |
| Publisher | : MIT Press |
| Total Pages | : 369 |
| Release | : 2024-08-06 |
| Genre | : Science |
| ISBN | : 0262552817 |
An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.
