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Delay Differential Equations

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Mathematics of Biology

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 80))

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Abstract

The purpose of these lectures is to survey parts of the theory of delay differential equations and functional differential equations that have been used or may be used in the modeling of biological phenomena. In the course of doing so, reference will be made from time to time to specific applications in biology, but primarily to illustrate the mathematical techniques. No attempt will be made to survey comprehensively any particular field in biology, since other lecturers here are doing so. We shall try to begin with elementary concepts of the theory, and yet to present some of the most recent results.

In the first lecture, I shall first indicate a few biological problems that give rise to delay differential equations, and give a large number of references. Then, since some of the audience may have only a slight acquaintance with such equations, I shall sketch their fundamental theory. Standard notations will be introduced and classifications of the equations into types (retarded, neutral, finite or infinite delay, etc.) will be described. Basic existence, uniqueness, continuation, and continuity theorems will be briefly described.

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  1. Pomona College, Claremont, CA, USA

    Kennet L. Cooke

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  1. Kennet L. Cooke
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Mimmo Iannelli

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Cooke, K.L. (2010). Delay Differential Equations. In: Iannelli, M. (eds) Mathematics of Biology. C.I.M.E. Summer Schools, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11069-6_1

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