A new class of planar differential systems with hyperbolic algebraic limit cycles

Authors

  • Fouad Khireddine Department of Mathematics, Faculty of Science, University of Boumerdes, Boumerdes, 35000, Algeria. https://orcid.org/0009-0007-9379-8734
  • Mohamed Grazem Department of Mathematics, Faculty of Science, University of Boumerdes, Boumerdes, 35000, Algeria.; Laboratory of Applied Mathematics, Faculty of Sciences, Setif 1 University Ferhat Abbas, Setif, 19000, Algeria. https://orcid.org/0000-0001-9410-6487
  • Ahmed Bendjeddou Laboratory of Applied Mathematics, Faculty of Sciences, Setif 1 University Ferhat Abbas, Setif, 19000, Algeria. https://orcid.org/0009-0002-6275-6957

Abstract

This work investigates a family of planar polynomial differential systems of degree n or greater. For these systems, we introduce invariant algebraic curves of degree n that can exhibit closed connected components. We prove that each bounded component of such curves defines a hyperbolic limit cycle for the system. Furthermore, several explicit examples are provided to illustrate the validity and geometric applicability of our main theorem.

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Published

2026-08-30

Issue

Vol. 33 No. 3 (2026): Nonlinear Studies

Section

Articles

License

Copyright (c) 2026 Fouad Khireddine, Mohamed Grazem, Ahmed Bendjeddou

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

A new class of planar differential systems with hyperbolic algebraic limit cycles. (2026). Nonlinear Studies, 33(3), 1031-1038. https://www.nonlinearstudies.com/index.php/nonlinear/article/view/4378