Limit cycles in piecewise polynomial Hamiltonian systems allowing nonlinear switching boundaries

Li, Tao; Llibre, Jaume

doi:10.1016/j.jde.2022.11.007

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…In [9], they study the limit cycles of the discontinuous piecewise differential systems separated by one straight line and formed by two polynomial Hamiltonian systems, and consequently, such limit cycles are algebraic. While in this paper, only one of the systems is Hamiltonian, otherwise the piecewise differential system cannot have limit cycles.…”

Section: Introductionmentioning

confidence: 99%

Limit Cycles of Polynomially Integrable Piecewise Differential Systems

García

Llibre

Río

et al. 2023

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In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. Under this assumption, piecewise differential systems have no more than one limit cycle. This study characterizes linear differential systems with polynomial first integrals.

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Section: Introductionmentioning

confidence: 99%

Limit Cycles of Polynomially Integrable Piecewise Differential Systems

García

Llibre

Río

et al. 2023

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The period annulus and limit cycles in a planar piecewise linear system defined in three zones separated by two parallel lines

Xiong,

2025

Journal of Differential Equations

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Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points

Sun,

2024

Int. J. Bifurcation Chaos

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In this paper, we investigate the existence and number of crossing limit cycles in a class of planar piecewise linear systems with node–node type critical points defined in two zones separated by a nonregular line formed by two rays emanated from the origin [Formula: see text], which are the positive [Formula: see text]- and [Formula: see text]-axes. We focus our attention on the existence of two-point crossing limit cycles, which intersect the switching line at two points. We obtain sufficient conditions under which the system has two two-point crossing limit cycles which intersect only one of the two rays. Moreover, we construct examples to show that this class of systems can have two, three or four two-point crossing limit cycles.

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Limit cycles in piecewise polynomial Hamiltonian systems allowing nonlinear switching boundaries

Cited by 4 publications

References 39 publications

Limit Cycles of Polynomially Integrable Piecewise Differential Systems

Limit Cycles of Polynomially Integrable Piecewise Differential Systems

The period annulus and limit cycles in a planar piecewise linear system defined in three zones separated by two parallel lines

Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points

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