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Coexistence of limit cycles in a septic planar differential system enclosing a non-elementary singular point, using Riccati equation

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Abstract

We give a new family of planar polynomial differential systems of degree seven with a non elementary point at the origin. We show the integrability of this family by transforming it into a Riccati equation. We determine sufficient conditions for the coexistence of algebraic and non-algebraic limit cycle surrounding this non elementary point. Moreover these limits cycles are explicitly given. An example is given and its phase portrait is drawn as an illustration of our result.

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Acknowledgements

We would like to thank the General Directory for Scientific Research and Technological Development (GDSRTD), MESRS Algeria and Research project under code: PRFUN C00L03UN190120220004, for their financial supports.

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Author notes

  1. R. Cheurfa and A. Bendjeddou have contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Applied Mathematics, Department of Mathematics, University Ferhat Abbas Sétif 1, Sétif, Algeria

    R. Allaoua, R. Cheurfa & A. Bendjeddou

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  1. R. Allaoua
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  2. R. Cheurfa
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  3. A. Bendjeddou
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Correspondence to R. Allaoua.

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Communicated by Marco Antonio Teixeira.

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Allaoua, R., Cheurfa, R. & Bendjeddou, A. Coexistence of limit cycles in a septic planar differential system enclosing a non-elementary singular point, using Riccati equation. São Paulo J. Math. Sci. 16, 997–1006 (2022). https://doi.org/10.1007/s40863-022-00310-2

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  • DOI: https://doi.org/10.1007/s40863-022-00310-2

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