A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system

DOI10.1007/s12346-020-00398-xzbMath1455.34037OpenAlexW3031125050MaRDI QIDQ2190826

Mao'an Han, Xiao-yan Chen

Publication date: 22 June 2020

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

Full work available at URL: https://doi.org/10.1007/s12346-020-00398-x

zbMATH Keywords

limit cycleMelnikov functionpiecewise smooth 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) 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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (5)

An estimate of the number of limit cycles bifurcating from a planar integrable system ⋮ The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines ⋮ Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system ⋮ Further study on Horozov-Iliev's method of estimating the number of limit cycles ⋮ Number of Limit Cycles from a Class of Perturbed Piecewise Polynomial Systems

Cites Work

• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle
• On the limit cycles of perturbed discontinuous planar systems with 4 switching lines
• Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations
• On the birth of limit cycles for non-smooth dynamical systems
• Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems
• A class of reversible quadratic systems with piecewise polynomial perturbations
• Limit cycles for discontinuous quadratic differential systems with two zones
• Averaging theory for discontinuous piecewise differential systems
• A Filippov system describing the effect of prey refuge use on a ratio-dependent predator-prey model
• A linear estimate of the number of limit cycles for some planar piecewise smooth quadratic differential system
• Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones
• Piecewise-smooth dynamical systems. Theory and applications
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system