THE SEPARATRIX VALUES OF A PLANAR HOMOCLINIC LOOP

DOI10.1142/S0218127409024037zbMath1176.34053MaRDI QIDQ3649635

Xuexing Wang, Lincheng Zhao

Publication date: 4 December 2009

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

zbMATH Keywords

normal formhomoclinic bifurcationsaddle valueseparatrix value

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Loop Numbers for the Stability of Homoclinic Loops of Planar Vector Fields ⋮ FRACTAL ANALYSIS OF HOPF BIFURCATION AT INFINITY

Cites Work

• The loop quantities and bifurcations of homoclinic loops
• Cyclicity of several planar graphics and ensembles through three singular points without generic conditions
• Global bifurcations in a perturbed cubic system with \(Z_ 2\)-symmetry
• Saddle quantities and applications
• Bifurcations of limit cycles in a cubic system
• 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
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• The generalized homoclinic bifurcation

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