Limit Cycles for a Class of Planar Differential Systems with a Degenerate Singular Point
Abstract
This paper investigates a class of planar differential systems characterized by a degenerate singular point. We demonstrate that this class is Liouville integrable and explicitly derive a first integral using an Abel equation of the second kind. Moreover, through an analysis based on the Poincaré return map, we establish the existence of two non-algebraic limit cycles or a single algebraic limit cycle near the degenerate point. The occurrence of these limit cycles is shown to depend sensitively on the system's parameters.
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Copyright (c) 2025 Abdelkrim Kna, Ahmed bendjeddou, Omar Chaalal, Akca Haydar
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