| Title:
|
Maximum number of limit cycles for generalized Liénard polynomial differential systems (English) |
| Author:
|
Berbache, Aziza |
| Author:
|
Bendjeddou, Ahmed |
| Author:
|
Benadouane, Sabah |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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146 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
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151-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider limit cycles of a class of polynomial differential systems of the form $$ \begin {cases} \dot {x}=y, \\ \dot {y}=-x-\varepsilon (g_{21}( x) y^{2\alpha +1} +f_{21}(x) y^{2\beta })-\varepsilon ^{2}(g_{22}( x) y^{2\alpha +1}+f_{22}( x) y^{2\beta }), \end {cases} $$ where $\beta $ and $\alpha $ are positive integers, $g_{2j}$ and $f_{2j}$ have degree $m$ and $n$, respectively, for each $j=1,2$, and $\varepsilon $ is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center $\dot {x}=y$, $\dot {y}=-x$ using the averaging theory of first and second order. (English) |
| Keyword:
|
polynomial differential system |
| Keyword:
|
limit cycle |
| Keyword:
|
averaging theory |
| MSC:
|
34C07 |
| MSC:
|
34C23 |
| MSC:
|
37G15 |
| DOI:
|
10.21136/MB.2020.0134-18 |
| . |
| Date available:
|
2021-05-20T13:53:01Z |
| Last updated:
|
2021-06-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148929 |
| . |
| Reference:
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