Titlebook: An Introduction to Delay Differential Equations with Applications to the Life Sciences; Hal Smith Textbook 2011 Springer Science+Business

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刚毅

Delayed Negative Feedback: A Warm-Up,n.We use it to illustrate features common to delay differential equations, such as the tendency of delays to give rise to oscillations that can become undamped if delays are large.The obstructions to solving delay differential equations backwards in time are readily appreciated for this simple equat

indigenous

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Linear Systems and Linearization, the system about the equilibrium and to determine exponential rates of growth and decay for the associated linear system. The framework for carrying this out is taken up in this chapter. Although the method is similar to that for ODEs, the characteristic equation is more complicated, typically havi

泛滥

Semidynamical Systems and Delay Equations,nterval. Omega limit sets are defined and shown to have the same properties as for ODEs, with minor exceptions, although they are subsets of C. The dynamics of the delayed logistic equation and the chemostat model are treated in detail. A special class of delay equations is shown to generate monoton

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Distributed Delay Equations and the Linear Chain Trick,w and from the point of view of mathematical tractability. A distributed delay is arguably more likely to capture reality than a discrete one. The special class of systems treated here has the feature that by introducing additional components it can be reduced to a system of ODEs. In particular, lin

nascent

Phage and Bacteria in a Chemostat,e assumption of a fixed latent period for virus inside the infected cell. The main biological issues addressed are the persistence and extinction of bacteria and of bacteriophage(phage). From a mathematical perspective, we focus on bifurcation of equilibria and Hopf bifurcation from the coexistence

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Introduction,ntial student projects. The reader should feel free to pick and choose to which of these to devote attention. Following this, some terminology is introduced and the reader is pointed to various computer software designed specifically for delay differential equations.

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