Geodesic
On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 617-629

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we have solved the extension of the 16th Hilbert problem to this class of differential systems.
DOI : 10.21136/MB.2022.0181-21
Classification : 34C05, 34C07, 37G15
Keywords: discontinuous piecewise differential system; continuous piecewise differential system; first integral; non-algebraic limit cycle; linear system; quadratic center 
@article{10_21136_MB_2022_0181_21,
     author = {Berbache, Aziza},
     title = {On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems},
     journal = {Mathematica Bohemica},
     pages = {617--629},
     publisher = {mathdoc},
     volume = {148},
     number = {4},
     year = {2023},
     doi = {10.21136/MB.2022.0181-21},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0181-21/}
}
TY  - JOUR
AU  - Berbache, Aziza
TI  - On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems
JO  - Mathematica Bohemica
PY  - 2023
SP  - 617
EP  - 629
VL  - 148
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0181-21/
DO  - 10.21136/MB.2022.0181-21
LA  - en
ID  - 10_21136_MB_2022_0181_21
ER  - 
%0 Journal Article
%A Berbache, Aziza
%T On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems
%J Mathematica Bohemica
%D 2023
%P 617-629
%V 148
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0181-21/
%R 10.21136/MB.2022.0181-21
%G en
%F 10_21136_MB_2022_0181_21
Berbache, Aziza. On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 617-629. doi: 10.21136/MB.2022.0181-21

Cité par Sources :