Impact limit cycles in the planar piecewise linear hybrid systems

DOI10.1016/j.cnsns.2022.107074zbMath1505.34027OpenAlexW4313399542MaRDI QIDQ2685740

Zhengkang Li, Xing Bo Liu

Publication date: 23 February 2023

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2022.107074

zbMATH Keywords

limit cyclelinear centerplanar piecewise linear hybrid systemreset map

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) 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)

Cites Work

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• Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones
• On the number of limit cycles in general planar piecewise linear systems
• Limit cycles in small perturbations of a planar piecewise linear Hamiltonian system with a non-regular separation line
• On Hopf bifurcation in non-smooth planar systems
• Piecewise linear differential systems with only centers can create limit cycles?
• Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
• Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
• An introduction to hybrid dynamical systems
• Limit sets of discontinuous vector fields on two-dimensional manifolds
• Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications
• Computation of periodic orbits for piecewise linear oscillator by harmonic balance methods
• Limit cycles and global dynamics of planar piecewise linear refracting systems of focus-focus type
• Limit cycles in the discontinuous planar piecewise linear systems with three zones
• On the Poincaré-Adronov-Melnikov method for the existence of grazing impact periodic solutions of differential equations
• A general mechanism to generate three limit cycles in planar Filippov systems with two zones
• Piecewise-smooth dynamical systems. Theory and applications
• Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle
• Limit cycles bifurcating from an invisible fold-fold in planar piecewise Hamiltonian systems
• The planar discontinuous piecewise linear refracting systems have at most one limit cycle
• Planar systems of piecewise linear differential equations with a line of discontinuity
• An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems
• One-Parameter Bifurcations in Planar Filippov Systems
• The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System
• Limit Cycles Induced by Threshold Nonlinearity in Planar Piecewise Linear Systems of Node-Focus or Node-Center Type
• Limit Cycles in Discontinuous Planar Piecewise Linear Systems Separated by a Nonregular Line of Center–Center Type
• Limit Cycles in Discontinuous Piecewise Linear Planar Hamiltonian Systems Without Equilibrium Points
• Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones
• Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities
• A periodically forced piecewise linear oscillator
• Dynamical properties of hybrid automata
• Limit cycles created by piecewise linear centers
• On Existence and Bifurcations of Periodic Motions in Discontinuous Dynamical Systems

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