Local dynamics of an equation with distributed delay

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 spec...

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Bibliographic Details
Published in:Differential equations 2014, Vol.50 (1), p.15-24
Main Author: Kashchenko, I. S.
Format: Article
Language:English
Subjects:
Analogs
Boundary value problems
Delay
Difference and Functional Equations
Differential equations
Distribution functions
Dynamic mechanical properties
Dynamic tests
Dynamics
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Neighborhoods
Ordinary Differential Equations
Partial Differential Equations
Studies
Theorems
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266114010030