The planar discontinuous piecewise linear refracting systems have at most one limit cycle

DOI10.1016/j.nahs.2021.101045zbMath1474.34286OpenAlexW3149668445MaRDI QIDQ2665303

Changjian Liu, Jaume Llibre, Shimin Li

Publication date: 19 November 2021

Published in: Nonlinear Analysis. Hybrid Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nahs.2021.101045

zbMATH Keywords

limit cyclepiecewise linear systemsrefracting systems

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

Global phase portraits of planar piecewise linear refracting systems of saddle-saddle type ⋮ Global studies on a continuous planar piecewise linear differential system with three zones ⋮ On the Poincaré-Bendixson index theorem for a class of piecewise linear differential systems ⋮ Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region ⋮ On the indices of singular points for planar bounded piecewise smooth polynomial vector field ⋮ Impact limit cycles in the planar piecewise linear hybrid systems ⋮ Cyclicity near infinity in piecewise linear vector fields having a nonregular switching line ⋮ Integral characterization for Poincaré half-maps in planar linear systems ⋮ Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line ⋮ On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center

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