Dynamics analysis of Llibre-Menezes piecewise linear systems

DOI10.1007/s12346-021-00542-1zbMath1493.34046OpenAlexW3217715288MaRDI QIDQ2073373

Xiao-Song Yang, Yuhong Zhang

Publication date: 2 February 2022

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-021-00542-1

zbMATH Keywords

limit cyclepiecewise linear systemsFilippov systemsMarkus-Yamabe conjecture

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Asymptotic properties of solutions to ordinary differential equations (34D05)

Cites Work

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• Maximum number of limit cycles for certain piecewise linear dynamical systems
• On the Kalman problem
• Global asymptotic stability of differential equations in the plane
• A polynomial counterexample to the Markus-Yamabe conjecture
• The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems
• Weakened Markus--Yamabe conditions for 2-dimensional global asymptotic stability
• A solution to the bidimensional global asymptotic stability conjecture
• Asymptotic stability of linearizations of a planar vector field with a singular point implies global stability
• The Markus-Yamabe conjecture does not hold for discontinuous piecewise linear differential systems separated by one straight line
• Piecewise-smooth dynamical systems. Theory and applications
• On Stability in the Large for Systems of Ordinary Differential Equations
• One-Parameter Bifurcations in Planar Filippov Systems
• A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
• Differential equations with discontinuous right-hand side

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