Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7

DOI10.1016/j.chaos.2015.01.009zbMath1352.34043OpenAlexW1964805101MaRDI QIDQ728377

A. Bakhshalizadeh, Rasoul Asheghi

Publication date: 20 December 2016

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2015.01.009

zbMATH Keywords

cuspidal loopnumber of limit cyclespolynomial Liénard systems

Mathematics Subject Classification ID

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (5)

Limit cycle bifurcations for a kind of Liénard system with degree seven ⋮ Limit cycles of a class of Liénard systems with restoring forces of seventh degree ⋮ Limit cycles near an eye-figure loop in some polynomial Liénard systems ⋮ The dynamics of a kind of Liénard system with sixth degree and its limit cycle bifurcations under perturbations ⋮ ON THE NUMBER OF LIMIT CYCLES FOR A QUINTIC LIÉNARD SYSTEM UNDER POLYNOMIAL PERTURBATIONS

Cites Work

• Computation of expansion coefficients of Melnikov functions near a nilpotent center
• Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop
• Limit cycles of some polynomial Liénard systems
• Uniqueness of limit cycles for Liénard differential equations of degree four
• On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems
• Bifurcations on a five-parameter family of planar vector field
• Estimating the number of limit cycles in polynomial systems
• Quadratic Liénard equations with quadratic damping
• Limit cycle bifurcations of some Liénard systems
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• Cubic Lienard equations with linear damping
• The number of small-amplitude limit cycles of Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• Complete hyperelliptic integrals of the first kind and their non-oscillation
• Centennial History of Hilbert's 16th Problem
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7