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Delay differential equations have numerous applications in science and engineering. This short, expository book offers a stimulating collection of examples of delay differential equations which are in use as models for a variety of phenomena in the life sciences, physics and technology, chemistry and economics. Avoiding mathematical proofs but offering more than one hundred illustrations, this book illustrates how bifurcation and asymptotic techniques can systematically be used to extract analytical information of physical interest. 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. Thomas Erneux was a professor in Applied Mathematics at Northwestern University from 1982 to 1993. He then joined the Department of Physics at the Université Libre de Bruxelles.

Delay differential equations -- Numerical solutions. --- Delay differential equations. --- Delay differential equations --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functional differential equations. --- Differential equations, Functional --- Delay equations (Differential equations) --- Delay functional differential equations --- Differential delay equations --- Differential equations --- Differential equations with lag --- Functional differential equations --- Retarded argument (Differential equations) --- Retarded differential equations --- Retarded functional differential equations --- Time-lag systems (Differential equations) --- Delay equations --- Retarded argument --- Time-lag equations --- Mathematics. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Ordinary Differential Equations. --- Mathematical Methods in Physics. --- Dynamical Systems and Ergodic Theory. --- Appl.Mathematics/Computational Methods of Engineering. --- Functional equations --- Differential Equations. --- Mathematical physics. --- Differentiable dynamical systems. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Physical mathematics --- Physics --- 517.91 Differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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Ergodic theory. Information theory --- Differential equations --- Mathematical physics --- Engineering sciences. Technology --- differentiaalvergelijkingen --- analyse (wiskunde) --- wiskunde --- ingenieurswetenschappen --- fysica --- informatietheorie

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Bridging the gap between laser physics and applied mathematics, this book offers a new perspective on laser dynamics. Combining fresh treatments of classic problems with up-to-date research, asymptotic techniques appropriate for nonlinear dynamical systems are shown to offer a powerful alternative to numerical simulations. The combined analytical and experimental description of dynamical instabilities provides a clear derivation of physical formulae and an evaluation of their significance. Starting with the observation of different time scales of an operating laser, the book develops approximation techniques to systematically explore their effects. Laser dynamical regimes are introduced at different levels of complexity, from standard turn-on experiments to stiff, chaotic, spontaneous or driven pulsations. Particular attention is given to quantitative comparisons between experiments and theory. The book broadens the range of analytical tools available to laser physicists and provides applied mathematicians with problems of practical interest, making it invaluable for graduate students and researchers.

Lasers. --- Lasers --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Mathematics. --- Dynamics. --- Mathematical models. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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