Applied delay differential equations / Thomas Erneux

Auteur: Erneux, Thomas - AuteurType de document: Livre numériqueCollection: Surveys and tutorials in the applied mathematical sciences ; 3Langue: anglaisÉditeur: Berlin : Springer, 2009 ISBN: 9780387743714 Note: This book is devoted to the theory and applications of time-delay differential equations, which is currently among the fastest-growing and most important areas of research. Avoiding rigorous mathematical proofs, but, at the same time, maintaining mathematical strictness in the presented material, the author shows challenging aspects of delay differential equations in a way understandable for readers. He shows in what way and why the equations appear in mathematical models and how to investigate them, namely, how to find their solution, provide bifurcation, asymptotic, and stability analyses, etc. The book is full of applications of delay differential equations to the natural and social sciences and engineering. The examples range from a mathematical description of pupil light reflex and sleep disorders to a depiction of a semiconductor laser system and its optoelectronic feedback and a portrayal of a regenerative effect for machine tool chatter. Numerous illustrations offered in the book play an essential role in the theoretical presentation that follows, as well as in helping readers to grasp applied issues. This book is written in a language suitable for undergraduate and graduate students who have calculus and differential equations courses in their background. It is an excellent guide book for mathematicians who construct and investigate mathematical models, as well as for multi-disciplinary scientists who apply mathematics to describe real-life phenomena in their research. It can also be used as a reference book on delay differential equations. (MathSciNet) Sujets MSC: 34K60 Ordinary differential equations -- Functional-differential and differential-difference equations -- Qualitative investigation and simulation of models
34K35 Ordinary differential equations -- Functional-differential and differential-difference equations -- Control problems
34C15 Ordinary differential equations -- Qualitative theory -- Nonlinear oscillations, coupled oscillators
65P30 Numerical analysis -- Numerical problems in dynamical systems -- Bifurcation problems
34K18 Ordinary differential equations -- Functional-differential and differential-difference equations -- Bifurcation theory
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This book is devoted to the theory and applications of time-delay differential equations, which is currently among the fastest-growing and most important areas of research. Avoiding rigorous mathematical proofs, but, at the same time, maintaining mathematical strictness in the presented material, the author shows challenging aspects of delay differential equations in a way understandable for readers. He shows in what way and why the equations appear in mathematical models and how to investigate them, namely, how to find their solution, provide bifurcation, asymptotic, and stability analyses, etc.
The book is full of applications of delay differential equations to the natural and social sciences and engineering. The examples range from a mathematical description of pupil light reflex and sleep disorders to a depiction of a semiconductor laser system and its optoelectronic feedback and a portrayal of a regenerative effect for machine tool chatter. Numerous illustrations offered in the book play an essential role in the theoretical presentation that follows, as well as in helping readers to grasp applied issues.
This book is written in a language suitable for undergraduate and graduate students who have calculus and differential equations courses in their background. It is an excellent guide book for mathematicians who construct and investigate mathematical models, as well as for multi-disciplinary scientists who apply mathematics to describe real-life phenomena in their research. It can also be used as a reference book on delay differential equations. (MathSciNet)

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