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Explicit formulas for two limit cycles of a family of planar differential systems
https://doi.org/10.26907/0021-3446-2025-4-71-79
Abstract
In this work, we study a family of multi-parameter polynomial differential systems of degree eleven. We prove that the considered family has an invariant algebraic curve, which is given explicitly. Subsequently, we demonstrate the integrability of these systems and derive an explicit expression for a first integral. Moreover, we provide sufficient conditions for the systems to possess two explicitly given limit cycles. The applicability of our results is illustrated by a concrete example.
About the Authors
S. E. Hamizi
Higher National School of Renewable Energies, Environment and Sustainable Development
Algeria
Algeria
Saad Eddine Hamizi
Batna, 05078
R. Boukoucha
University of Bejaia
Algeria
Algeria
Rachid Boukoucha
Bejaia, 06000
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Review
For citations:
Hamizi S.E., Boukoucha R. Explicit formulas for two limit cycles of a family of planar differential systems. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(4):71-79. (In Russ.) https://doi.org/10.26907/0021-3446-2025-4-71-79
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