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Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants. / Kryzhevich, S.G.

In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, No. 2, 2012, p. 106-128.

Research output: Contribution to journalArticle

Harvard

Kryzhevich, SG 2012, 'Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants', ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, no. 2, pp. 106-128. <http://www.math.spbu.ru/diffjournal/RU/numbers/2012.2/article.1.8.html>

APA

Kryzhevich, S. G. (2012). Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ, (2), 106-128. http://www.math.spbu.ru/diffjournal/RU/numbers/2012.2/article.1.8.html

Vancouver

Kryzhevich SG. Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants. ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2012;(2):106-128.

Author

Kryzhevich, S.G. / Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants. In: ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ. 2012 ; No. 2. pp. 106-128.

BibTeX

@article{af608d2e90cf4521aa5ce5a23f05eca0,
title = "Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants",
abstract = "An autonomous discontinuous system, defined by a set of vector fields on a compact manifold is studied. A multigraph, describing possible transitions of trajectories from one cell to another, is constructed. It is shown that there exists a canonical algorithm allowing to reduce this graph to its canonical form which is the same for all topologically conjugated systems of vector fields and persists under perturbations of general systems of vector fields. Bifurcations, leading to changing of the normal form of the corresponding graph, are studied.",
keywords = "Partitions, cell dynamics, discontinuous systems.",
author = "S.G Kryzhevich",
year = "2012",
language = "English",
pages = "106--128",
journal = "ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ",
issn = "1817-2172",
publisher = "Электронный журнал {"}Дифференциальные уравнения и процессы управления{"}",
number = "2",

}

RIS

TY - JOUR

T1 - Mathematical Models of Discontinuous Dynamical Systems and their Geometric Invariants

AU - Kryzhevich, S.G

PY - 2012

Y1 - 2012

N2 - An autonomous discontinuous system, defined by a set of vector fields on a compact manifold is studied. A multigraph, describing possible transitions of trajectories from one cell to another, is constructed. It is shown that there exists a canonical algorithm allowing to reduce this graph to its canonical form which is the same for all topologically conjugated systems of vector fields and persists under perturbations of general systems of vector fields. Bifurcations, leading to changing of the normal form of the corresponding graph, are studied.

AB - An autonomous discontinuous system, defined by a set of vector fields on a compact manifold is studied. A multigraph, describing possible transitions of trajectories from one cell to another, is constructed. It is shown that there exists a canonical algorithm allowing to reduce this graph to its canonical form which is the same for all topologically conjugated systems of vector fields and persists under perturbations of general systems of vector fields. Bifurcations, leading to changing of the normal form of the corresponding graph, are studied.

KW - Partitions

KW - cell dynamics

KW - discontinuous systems.

M3 - Article

SP - 106

EP - 128

JO - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ И ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1817-2172

IS - 2

ER -

ID: 5404910