Geodesic
Modeling of gradient-like flows on $n$-sphere
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 27 (2019) no. 6, pp. 63-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

A general idea of the qualitative study of dynamical systems, going back to the works by A. Andronov, E. Leontovich, A. Mayer, is a possibility to describe dynamics of a system using combinatorial invariants. So M. Peixoto proved that the structurally stable flows on surfaces are uniquely determined, up to topological equivalence, by the isomorphic class of a directed graph. Multidimensional structurally stable flows does not allow entering their classification into the framework of a general combinatorial invariant. However, for some subclasses of such systems it is possible to achieve the complet combinatorial description of their dynamics. In the present paper, based on classification results by S. Pilyugin, A. Prishlyak, V. Grines, E. Gurevich, O. Pochinka, any connected bi-color tree implemented as gradient-like flow of $n$-sphere, $n>2$ without heteroclinic intersections. This problem is solved using the appropriate gluing operations of the so-called Cherry boxes to the flow-shift. This result not only completes the topological classification for such flows, but also allows to model systems with a regular behavior. For such flows, the implementation is especially important because they model, for example, the reconnection processes in the solar corona.
Keywords: gradient-like flow, modeling. 
@article{IVP_2019_27_6_a4,
     author = {O. V. Pochinka and S. Yu. Galkina and D. D. Shubin},
     title = {Modeling of gradient-like flows on $n$-sphere},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {63--72},
     publisher = {mathdoc},
     volume = {27},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2019_27_6_a4/}
}
TY  - JOUR
AU  - O. V. Pochinka
AU  - S. Yu. Galkina
AU  - D. D. Shubin
TI  - Modeling of gradient-like flows on $n$-sphere
JO  - Izvestiya VUZ. Applied Nonlinear Dynamics
PY  - 2019
SP  - 63
EP  - 72
VL  - 27
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVP_2019_27_6_a4/
LA  - ru
ID  - IVP_2019_27_6_a4
ER  - 
%0 Journal Article
%A O. V. Pochinka
%A S. Yu. Galkina
%A D. D. Shubin
%T Modeling of gradient-like flows on $n$-sphere
%J Izvestiya VUZ. Applied Nonlinear Dynamics
%D 2019
%P 63-72
%V 27
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVP_2019_27_6_a4/
%G ru
%F IVP_2019_27_6_a4
O. V. Pochinka; S. Yu. Galkina; D. D. Shubin. Modeling of gradient-like flows on $n$-sphere. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 27 (2019) no. 6, pp. 63-72. http://geodesic.mathdoc.fr/item/IVP_2019_27_6_a4/