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Part of the book series: Applied Mathematical Sciences ((AMS,volume 182))

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Abstract

In this chapter we study general non-autonomous delay differential equations of the form

$$\dot{x}(t) = F(t,x(t),x(t - \rho (t))).$$

Our intention is to demonstrate how pullback attractors can be used to investigate the behaviour of such models. In particular, following the ideas in the preceding chapters we are able to compare the dynamics of systems of ordinary differential equations with that of the same system with a small delay and show that the associated attractors are upper semicontinuous as the delay tends to zero.

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Carvalho, A.N., Langa, J.A., Robinson, J.C. (2013). Delay differential equations. In: Attractors for infinite-dimensional non-autonomous dynamical systems. Applied Mathematical Sciences, vol 182. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4581-4_10

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