Abstract
We study the properties of the local dynamics of a differential equation with a distributed delay. We consider two forms of distribution functions, exponential and linear. We indicate parameters for which critical cases take place. It is shown that critical cases have an infinite dimension, and special equations describing the dynamics of the original problem (analogs of normal forms) are constructed in each critical case. The results on the correspondence of solutions of quasinormal forms and the original equation are represented.
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