Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle

DOI10.1142/S0218127416501807zbMath1349.34102OpenAlexW2543950809MaRDI QIDQ2834943

A. Bakhshalizadeh, Hamid R. Z. Zangeneh, Rasool Kazemi

Publication date: 1 December 2016

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

Full work available at URL: https://doi.org/10.1142/s0218127416501807

zbMATH Keywords

limit cyclesMelnikov functionheteroclinic loopChebyshev property

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, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (2)

Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems ⋮ On the number of limit cycles bifurcated from some Hamiltonian systems with a non-elementary heteroclinic loop

Cites Work

• Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system
• Bifurcation of limit cycles from a heteroclinic loop with a cusp
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle
• Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop
• Bounding the number of zeros of certain abelian integrals
• On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems
• Normal forms, Melnikov functions and bifurcations of limit cycles
• Limit cycles of differential equations
• On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• LIMIT CYCLE BIFURCATIONS NEAR A DOUBLE HOMOCLINIC LOOP WITH A NILPOTENT SADDLE
• HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
• Bifurcation of Limit Cycles in Small Perturbation of a Class of Liénard Systems
• Cubic Liénard equations with quadratic damping having two antisaddles

This page was built for publication: Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle