Limit Cycles in Discontinuous Piecewise Linear Planar Hamiltonian Systems Without Equilibrium Points

DOI10.1142/S021812742250153XOpenAlexW4293660554WikidataQ114072968 ScholiaQ114072968MaRDI QIDQ5043870

Zhengkang Li, Xing Bo Liu

Publication date: 6 October 2022

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812742250153x

zbMATH Keywords

limit cycleHamiltonian vector fieldfirst integraldiscontinuous piecewise linear planar system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Linear ordinary differential equations and systems (34A30) 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) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (1)

Impact limit cycles in the planar piecewise linear hybrid systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems
• 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?
• Piecewise linear differential systems without equilibria produce limit cycles?
• Limit cycles in planar piecewise linear differential systems with nonregular separation line
• Bifurcation theory for finitely smooth planar autonomous differential systems
• One- and two-hump solutions of a singularly perturbed cubic nonlinear Schrödinger equation
• Global dynamics of hybrid van der Pol-Rayleigh oscillators
• Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary
• Two limit cycles for a class of discontinuous piecewise linear differential systems with two pieces
• Limit cycles in the discontinuous planar piecewise linear systems with three zones
• Limit cycles of a class of discontinuous planar piecewise linear systems with three regions of Y-type
• On the Poincaré-Adronov-Melnikov method for the existence of grazing impact periodic solutions of differential equations
• Piecewise-smooth dynamical systems. Theory and applications
• Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems
• On piecewise linear differential systems with \(n\) limit cycles of arbitrary multiplicities in two zones
• Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle
• 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
• Diffusion‐driven codimension‐2 Turing–Hopf bifurcation in the general Brusselator model
• Limit Cycles in Planar Piecewise Linear Hamiltonian Systems with Three Zones Without Equilibrium Points
• The Number of Limit Cycles Bifurcating from a Degenerate Center of Piecewise Smooth Differential Systems
• Limit Cycles in Discontinuous Planar Piecewise Linear Systems Separated by a Nonregular Line of Center–Center Type
• The Extended 16th Hilbert Problem for Discontinuous Piecewise Linear Centers Separated by a Nonregular Line
• Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line
• Limit cycles created by piecewise linear centers
• LIMIT CYCLES OF PIECEWISE LINEAR DYNAMICAL SYSTEMS WITH THREE ZONES AND LATERAL SYSTEMS
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system
• The focus case of a nonsmooth Rayleigh-Duffing oscillator

This page was built for publication: Limit Cycles in Discontinuous Piecewise Linear Planar Hamiltonian Systems Without Equilibrium Points