On the cyclicity of a 2-polycycle for quadratic systems

DOI10.1016/j.chaos.2004.07.008zbMath1081.34512OpenAlexW2019178746MaRDI QIDQ1771748

Cheng Yang, Mao'an Han

Publication date: 18 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.07.008

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

Related Items (4)

Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle ⋮ Global bifurcation of a perturbed double-homoclinic loop ⋮ Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle ⋮ Limit cycles near homoclinic and heteroclinic loops

Cites Work

• Unnamed Item
• Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
• On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
• Cyclicity of planar homoclinic loops and quadratic integrable systems
• Cyclicity of homoclinic loops and degenerate cubic Hamiltonians
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation
• Elementary graphics of cyclicity 1 and 2
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Persistence of invariant tori in generalized Hamiltonian systems

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