Explicit limit cycles of a family of polynomial differential systems

Date

2017-09-13

Authors

Boukoucha, Rachid

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We consider the family of polynomial differential systems x' = x + (αy - βx) (αx2 - bxy + αy2)n, y' = y - (βy + αx) (αx2 - bxy + αy2)n, where α, b, ɑ, β 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.

Description

Keywords

Planar polynomial differential system, First integral, Algebraic limit cycles, Non-algebraic limit cycle

Citation

Boukoucha, R. (2017). Explicit limit cycles of a family of polynomial differential systems. <i>Electronic Journal of Differential Equations, 2017</i>(217), pp. 1-7.

Rights

Attribution 4.0 International

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