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| The singular limit of large delay in a DDE is relevant for a variety of applied problems. In several examples of such equations it has been demonstrated by formal asymptotics that the dynamics close to the destabilization of an equilibrium can be described by an amplitude equation of Ginzburg-Landau type. We present here some recent results that provide a more general and rigorous framework for this phenomenon. Based on a general theory for the spectrum of linearized DDEs with large dealy, we classify possible types of instabilities and provide for certain cases of this general framework a rigorous result about the validity of the amplitude equation. In particular, we discuss similarities and differences to analogous results about the validity of amplitude equations for spatially extended systems. |
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