Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. More...
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| Format: | Article |
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| Language: | English |
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University of Tehran
2006-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31768_b98c805ccf615f5486e5288a73e4b49f.pdf |
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| description | We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle. |
| format | Article |
| id | doaj-art-d9e927416c2042d384f78b9fe1379a2e |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2006-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-d9e927416c2042d384f78b9fe1379a2e2025-08-20T03:54:07ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142006-09-0117331768Relationships between Darboux Integrability and Limit Cycles for a Class of Able EquationsWe consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.https://jsciences.ut.ac.ir/article_31768_b98c805ccf615f5486e5288a73e4b49f.pdf |
| spellingShingle | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations Journal of Sciences, Islamic Republic of Iran |
| title | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations |
| title_full | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations |
| title_fullStr | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations |
| title_full_unstemmed | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations |
| title_short | Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations |
| title_sort | relationships between darboux integrability and limit cycles for a class of able equations |
| url | https://jsciences.ut.ac.ir/article_31768_b98c805ccf615f5486e5288a73e4b49f.pdf |