Home > Articles > Published articles > Darboux integrability and Algebraic limit cycles for a class of polynomial differential Systems |
Date: | 2014 |
Abstract: | This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems ˙x = λx − y + Pn+1(x, y) + xF2n(x, y), ˙y = x + λy + Qn+1(x, y)+yF2n(x, y), where Pi(x, y), Qi(x, y) and Fi(x, y) are homogeneous polynomials of degree i. Inside this class we identify some new Darboux integrable systems having either a focus or a center at the origin. For such Darboux integrable systems having degrees 5 and 9 we give the explicit expressions of their algebraic limit cycles. For the systems having degrees 3, 5, 7 and 9 we present necessary and sufficient conditions for being Darboux integrable. |
Grants: | Ministerio de Economía y Competitividad MTM2005-06098-C02-01 Ministerio de Economía y Competitividad SAB2006-0098 |
Note: | Agraïments: The first and third authors are partially supported by NNSF of China grant No. 10671123 and by a CICYT grant No. 2005SGR 00550. The third author is also partially supported by NCET of China grant No. 050391. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Algebraic limit cycles ; Darboux first integral |
Published in: | Science China Mathematics, Vol. 57 Núm. 4 (2014), p. 775-794, ISSN 1869-1862 |
Postprint 25 p, 696.1 KB |