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Integrability and limit cycles for a class of multi-parameter differential systems with unstable node point

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Abstract

We exhibit a class of non-linear planar polynomial differential systems. We show that this class has a first integral and we give the explicit expression of them and we discuss the existence of two limit cycles surrounding an unstable node according to the parameters of these systems.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, Faculty of Sciences, University Ferhat Abbas Sétif 1, Algeria, 19 000, Sétif, Algeria

    A. Kina & A. Bendjeddou

  2. Department of Mathematics and Computer Science, University of Ghardaia, 47 000, Bounoura, Algeria

    A. Kina

  3. Department of Mathematics, University of Bordj Bou Arréridj, 34 265, El Anceur, Algeria

    A. Berbache

Authors
  1. A. Kina
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  2. A. Berbache
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  3. A. Bendjeddou
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Correspondence to A. Kina.

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Kina, A., Berbache, A. & Bendjeddou, A. Integrability and limit cycles for a class of multi-parameter differential systems with unstable node point. Rend. Circ. Mat. Palermo, II. Ser 72, 1937–1946 (2023). https://doi.org/10.1007/s12215-022-00774-3

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  • DOI: https://doi.org/10.1007/s12215-022-00774-3

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