Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\)

DOI10.1016/j.jde.2018.07.042zbMath1406.34068OpenAlexW2883913766MaRDI QIDQ1993971

Junmin Yang, Mao'an Han, Pei Yu

Publication date: 6 November 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.07.042

zbMATH Keywords

bifurcationlimit cycleMelnikov functionnilpotent saddlenear-Hamiltonian 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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (8)

Limit cycle bifurcations for a kind of Liénard system with degree seven ⋮ Some properties of Melnikov functions near a cuspidal loop ⋮ On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order \(m\) ⋮ On the Number of Limit Cycles Bifurcating from a Compound Polycycle ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \) ⋮ On the number of limit cycles of a quartic polynomial system ⋮ BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computation of expansion coefficients of Melnikov functions near a nilpotent center
• Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
• Limit cycles of differential equations
• Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle
• On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems
• Bifurcations of invariant tori and subharmonic solutions for periodic perturbed systems
• Abelian integrals for cubic vector fields
• Limit cycle bifurcations by perturbing a compound loop with a cusp and a nilpotent saddle
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles
• The perturbations of a class of hyper-elliptic Hamilton systems with a double homoclinic loop through a nilpotent saddle
• On the Distribution of Limit Cycles in a Liénard System with a Nilpotent Center and a Nilpotent Saddle
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER
• Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a Cuspidal Loop of Order m
• Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop

This page was built for publication: Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\)