Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system

DOI10.1016/j.na.2011.09.044zbMath1244.34048OpenAlexW2085569884MaRDI QIDQ412647

Rasool Kazemi, Ali Atabaigi, Hamid R. Z. Zangeneh

Publication date: 4 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.09.044

zbMATH Keywords

limit cyclesMelnikov functionHilbert's 16th problemcuspidal loop of order 2near-Hamiltonian systems

Mathematics Subject Classification ID

Related Items (16)

Bifurcation of limit cycles from a heteroclinic loop with two cusps ⋮ Limit Cycle Bifurcations Near a Heteroclinic Loop with Two Nilpotent Cusps of General Order ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp ⋮ 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 \(m\) ⋮ Limit cycles bifurcating from periodic orbits near a centre and a homoclinic loop with a nilpotent singularity of Hamiltonian systems ⋮ Bifurcation of limit cycles near a heteroclinic loop with nilpotent cusps ⋮ Limit cycle bifurcations by perturbing a compound loop with a cusp and a nilpotent saddle ⋮ Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a 3-Polycycle Having a Cusp of Order One or Two ⋮ Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order \(m\) ⋮ On the number of limit cycles bifurcated from some Hamiltonian systems with a non-elementary heteroclinic loop ⋮ On the monotonicity of the ratio of some hyperelliptic integrals of order 7 ⋮ Analytical approximation of cuspidal loops using a nonlinear time transformation method ⋮ Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle ⋮ Limit Cycle Bifurcations by Perturbing a Hamiltonian System with a Cuspidal Loop of Order m ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Cites Work

• Unnamed Item
• Limit cycles near homoclinic and heteroclinic loops
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Melnikov functions for period annulus, nondegenerate centers, heteroclinic and homoclinic cycles.
• Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system
• Some bifurcation methods of finding limit cycles
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Bifurcations of cuspidal loops
• Elementary graphics of cyclicity 1 and 2

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