Limit cycle bifurcations near a 2-polycycle or double 2-polycycle of planar systems

DOI10.1016/j.na.2013.10.019zbMath1288.34037OpenAlexW2003303008MaRDI QIDQ2637060

Junmin Yang, Yanqin Xiong, Mao'an Han

Publication date: 18 February 2014

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.2013.10.019

zbMATH Keywords

bifurcationhomoclinic loopheteroclinic loopnear-Hamiltonian systemalien limit cycle2-polycycle

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (12)

Analysis of a Shil'nikov type homoclinic bifurcation ⋮ Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle ⋮ Limit cycle bifurcations near a double 2-polycycle on the cylinder ⋮ Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points ⋮ On the Number of Limit Cycles Bifurcating from a Compound Polycycle ⋮ Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems ⋮ Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle ⋮ Heterodimensional cycle bifurcation with two orbit flips ⋮ Special cubic perturbations of the Duffing oscillator \(x=x-x^3\) near the eight-loop ⋮ Limit cycle bifurcations near homoclinic and heteroclinic loops via stability-changing of a homoclinic loop ⋮ Generic unfolding of a degenerate heterodimensional cycle ⋮ BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES

Cites Work

• Normal forms, Melnikov functions and bifurcations of limit cycles
• Perturbations of symmetric elliptic Hamiltonians of degree four
• The loop quantities and bifurcations of homoclinic loops
• Detecting alien limit cycles near a Hamiltonian 2-saddle cycle
• Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Alien limit cycles near a Hamiltonian 2-saddle cycle
• Saddle quantities and applications
• On the stability of double homoclinic and heteroclinic cycles.
• Alien limit cycles in Liénard equations
• On the number of limit cycles which appear by perturbation of Hamiltonian two-saddle cycles of planar vector fields
• Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
• Abelian integrals and limit cycles
• Existence of at most 1, 2, or 3 zeros of a Melnikov function and limit cycles

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