Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems
We perturb the differential system x˙1=-x2(1+x1), x˙2=x1(1+x1), and x˙k=0 for k=3,…,d inside the class of all polynomial differential systems of degree n in Rd, and we prove that at most nd-1 limit cycles can be obtained for the perturbed system using the first-order averaging theory.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/1868027 |
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| _version_ | 1832565096747892736 |
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| author | Zouhair Diab Amar Makhlouf |
| author_facet | Zouhair Diab Amar Makhlouf |
| author_sort | Zouhair Diab |
| collection | DOAJ |
| description | We perturb the differential system x˙1=-x2(1+x1), x˙2=x1(1+x1), and x˙k=0 for k=3,…,d inside the class of all polynomial differential systems of degree n in Rd, and we prove that at most nd-1 limit cycles can be obtained for the perturbed system using the first-order averaging theory. |
| format | Article |
| id | doaj-art-4f5b0fdfc9874c0cbe2f9171e6cab3bf |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4f5b0fdfc9874c0cbe2f9171e6cab3bf2025-02-03T01:09:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/18680271868027Limit Cycles for the Class of D-Dimensional Polynomial Differential SystemsZouhair Diab0Amar Makhlouf1Department of Mathematics, University of Tébessa, 12002 Tébessa, AlgeriaDepartment of Mathematics, Faculty of Sciences, UBM of Annaba, El Hadjar, 23000 Annaba, AlgeriaWe perturb the differential system x˙1=-x2(1+x1), x˙2=x1(1+x1), and x˙k=0 for k=3,…,d inside the class of all polynomial differential systems of degree n in Rd, and we prove that at most nd-1 limit cycles can be obtained for the perturbed system using the first-order averaging theory.http://dx.doi.org/10.1155/2016/1868027 |
| spellingShingle | Zouhair Diab Amar Makhlouf Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems Journal of Applied Mathematics |
| title | Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems |
| title_full | Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems |
| title_fullStr | Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems |
| title_full_unstemmed | Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems |
| title_short | Limit Cycles for the Class of D-Dimensional Polynomial Differential Systems |
| title_sort | limit cycles for the class of d dimensional polynomial differential systems |
| url | http://dx.doi.org/10.1155/2016/1868027 |
| work_keys_str_mv | AT zouhairdiab limitcyclesfortheclassofddimensionalpolynomialdifferentialsystems AT amarmakhlouf limitcyclesfortheclassofddimensionalpolynomialdifferentialsystems |