Applied Delay Differential Equations

By: Thomas Erneux

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Paperback | 1 December 2008

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220 Pages

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23.5 x 15.88 x 1.91

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Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

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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. ... 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 ... as well as for multi-disciplinary scientists who apply mathematics to describe real-life phenomena in their research. ... used as a reference book on delay differential equations." (Natali Hritonenko, Mathematical Reviews, Issue 2009 m)

"Thomas Erneux has written an outstanding book that brings a refreshing approach to the subject, an approach utilizing asymptotic and bifurcation techniques that are accessible to a wide scientific audience. ... book could be used in a course on DDEs at the advance undergraduate or graduate level ... . I highly recommend the book to students and researchers ... . Applied Delay Differential Equations is highly accessible and the mathematical techniques presented are sufficient to extract valuable insights into DDEs and their applications." (Steven M. Baer, SIAM Reviews, Vol. 53 (2), 2011)

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Introduction	p. 1
Properties	p. 2
Oscillations	p. 2
Short time solution	p. 3
Cyclic behaviors	p. 5
Car-following models	p. 7
Population dynamics	p. 9
Nonlinear optics	p. 13
Fluid dynamics	p. 15
Economics	p. 17
Mechanical engineering	p. 20
Combustion engines	p. 22
Classes of DDEs	p. 23
Delay recruitment equation	p. 24
Harmonic oscillator with delay	p. 24
Analytical tools	p. 27
Stability	p. 29
The characteristic equation	p. 30
Roots	p. 31
Hopf bifurcation point	p. 32
Position control and sampling	p. 33
Reduction of payload oscillations	p. 36
Traffic stability	p. 39
Car-following models	p. 39
Local and asymptotic stability	p. 42
Bistability	p. 43
Metastability	p. 46
Biology	p. 49
Population periodic cycles	p. 50
The Hopf bifurcation	p. 52
Time-delayed negative feedback	p. 56
Circulating red blood cells	p. 56
Pupil light reflex	p. 59
Periodic breathing	p. 62
Genetic oscillations	p. 63
Human postural control	p. 68
The inverted pendulum	p. 71
Bernoulli's equation	p. 75
The clarinet	p. 76
Sleep disorders	p. 81
Cascaded control of a liquid level system	p. 85
Chemistry	p. 91
Illuminated thermochemical reaction	p. 93
Reformulation	p. 93
Feedback	p. 95
The bistable iodate-arsenous acid reaction	p. 97
Weak delayed feedback	p. 100
Experiments	p. 100
A piecewise linear oscillator	p. 103
Mechanical vibrations	p. 109
Control engineering	p. 109
The method of multiple scales	p. 111
Minorsky's equation	p. 113
Hopf bifurcation	p. 113
Hopf bifurcation for large delay	p. 114
Torus bifurcation	p. 116
Map	p. 117
Large delay asymptotics: Ginzburgh-Landau equation	p. 118
Johnson and Moon's equation	p. 122
Unusual Hopf bifurcation	p. 123
Machine tool vibrations	p. 125
Formulation and stability	p. 126
Experiments	p. 130
Linear theory	p. 131
Nonlinear theory	p. 132
Lasers	p. 135
Optoelectronic feedback	p. 136
Delayed incoherent feedback	p. 138
Small feedback rate	p. 138
Moderate feedback rate	p. 142
Bifurcation near a double Hopf point	p. 146
Delayed coherent feedback	p. 152
Single-mode solutions	p. 155
Two mode solutions and mode beating	p. 156
Numerical simulations and bridges	p. 157
Imaging using OFB	p. 160
Stability analysis	p. 161
Low feedback rate approximation	p. 162
Optoelectronic oscillators	p. 165
Phase equations	p. 169
Weakly coupled oscillators	p. 171
Basic solutions	p. 171
Experiments	p. 175
Strongly coupled oscillators	p. 176
References	p. 181
Index	p. 201
Table of Contents provided by Ingram. All Rights Reserved.

Applied Delay Differential Equations

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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