BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION

DOI10.1142/S0218127408020847zbMath1147.34324OpenAlexW2118185506MaRDI QIDQ3536126

Fengjie Geng, Dan Liu, De-Ming Zhu

Publication date: 17 November 2008

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

Full work available at URL: https://doi.org/10.1142/s0218127408020847

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (10)

Bifurcations of Two-Dimensional Global Invariant Manifolds near a Noncentral Saddle-Node Homoclinic Orbit ⋮ Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ On the existence of bifocal heteroclinic cycles in a class of four-dimensional piecewise affine systems ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ BIFURCATIONS OF 2-2-1 HETERODIMENSIONAL CYCLES UNDER TRANSVERSALITY CONDITION ⋮ Bifurcation analysis of the multiple flips homoclinic orbit ⋮ Resonant homoclinic flips bifurcation in principal eigendirections ⋮ Codimension-4 resonant homoclinic bifurcations with orbit flips and inclination flips

Cites Work

• Bifurcations of rough heteroclinic loop with two saddle points
• Bifurcations of heteroclinic loops
• Degenerated homoclinic bifurcations with higher dimensions
• Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
• Inclination-flip homoclinic orbits arising from orbit-flip
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• CODIMENSION 3 HOMOCLINIC BIFURCATION OF ORBIT FLIP WITH RESONANT EIGENVALUES CORRESPONDING TO THE TANGENT DIRECTIONS
• Resonant homoclinic flip bifurcations

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