Research output: Contribution to journal › Article
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 journal › Article
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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