We consider the family of polynomial differential systems
where a, b, , are real constants and n is positive integer. We prove that these systems are Liouville integrable. Moreover, we determine sufficient conditions for the existence of an explicit algebraic or non-algebraic limit cycle. Examples exhibiting the applicability of our result are introduced.
Submitted October 4, 2016. Published September 13, 2017.
Math Subject Classifications: 34A05, 34C05, 34CO7, 34C25.
Key Words: Planar polynomial differential system; first integral; Algebraic limit cycle; non-algebraic limit cycle.
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| Rachid Boukoucha |
Department of Technology
Faculty of Technology
University of Bejaia
06000 Bejaia, Algeria
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