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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2021 Volume 18, Issue 1, Pages 1–8 (Mi semr1342)

Differentical equations, dynamical systems and optimal control

Kolmogorov differential systems with prescribed algebraic limit cycles

R. Chouader, S. Benyoucef, A. Bendjeddou

Laboratory of Applied Mathematics, Department of Mathematics, University of Setif 1, 19000, Algeria

Abstract: For a given algebraic curve, we exhibit Kolmogorov differential systems, and we show that these systems admit precisely the bounded components of the curve as hyperbolic limit cycles if certain conditions on the parameters of the system are satisfied.

Keywords: Sixteenth problem of Hilbert, planar differential system, invariant curve, periodic solution, hyperbolic limit cycle.

UDC: 517.9

MSC: 34C25, 34C05, 34C07

Received October 24, 2020, published January 12, 2021

Language: English

DOI: 10.33048/semi.2021.18.001



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© Steklov Math. Inst. of RAS, 2024