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Invariant manifolds of nonautonomous models neural networks

M.L. Kolomiets1, A.N. Sakharov2

AnnotationWe consider the problem of the Structure of invariant sets in nonautonomous systems describing the dynamics of neural networks. It is shown that normal hyperbolic manifolds of non-linear extensions of quasiperiodic flows on the torus is a bundle over the torus with a homogeneous space of compact matrix Lie group as a fiber.
Keywordsflows extensions on compact spaces, normally hyperbolic diversity, attractors, minimal sets, neural networks

1Assistant professor of department of higher mathematics, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; math@agri.sci-nnov.ru.

2Assistant professor of department of higher mathematic, Nizhny Novgorod State Agricultural Academy, Nizhny Novgorod; ansakharov2008@yandex.ru.

Citation: M.L. Kolomiets, A.N. Sakharov, "[Invariant manifolds of nonautonomous models neural networks]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:2 (2012) 74–80 (In Russian)