ON LIMIT CYCLES OF PIECEWISE DIFFERENTIAL SYSTEMS AND A CLASS OF QUADRATIC SYSTEMS

被引：0
|
作者：
Berbache, Aziza [1 ]
Anasser, El [1 ]
机构：
[1] Univ Mohamed El Bachir El Ibrahimi Bordj Bou Arrer, Fac Math & Informat, Dept Math, El Anasser 34265, Algeria
来源：
MATHEMATICA BOHEMICA | 2022年
关键词：
discontinuous piecewise differential system; continuous piecewise differential system; first integral; non-algebraic limit cycle; linear system; quadratic center;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：13
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