Geodesic
Local dynamics of equations with large delay
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2141-2150

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The local dynamics of a differential equation with large delay is analyzed using the normal forms technique. It is shown that, in the critical cases, families of parabolic equations play the role of infinite-dimensional normal forms. It is demonstrated analytically that even a very simple first-order delay equation can have a complicated dynamical behavior. Methods for constructing classes of stable modes for such equations are described. The proposed methods are extended for the case of secondorder equations. 
@article{ZVMMF_2008_48_12_a6,
     author = {I. S. Kashchenko},
     title = {Local dynamics of equations with large delay},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2141--2150},
     publisher = {mathdoc},
     volume = {48},
     number = {12},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a6/}
}
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I. S. Kashchenko. Local dynamics of equations with large delay. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2141-2150. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a6/