Homoclinic bifurcation with nonhyperbolic equilibria

DOI10.1016/j.na.2006.04.014zbMath1124.34025OpenAlexW2065034950MaRDI QIDQ876967

Xianlong Fu, Xing Bo Liu, De-Ming Zhu

Publication date: 19 April 2007

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.2006.04.014

zbMATH Keywords

periodic orbithomoclinic orbitPoincaré mappitchfork bifurcationlocal coordinate system

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 orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (7)

Bifurcations of Two-Dimensional Global Invariant Manifolds near a Noncentral Saddle-Node Homoclinic Orbit ⋮ Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation ⋮ Bifurcation of nongeneric homoclinic orbit accompanied by pitchfork bifurcation ⋮ Modeling and analysis of dynamics for a 3D mixed Lorenz system with a damped term ⋮ Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium ⋮ Bifurcation Complexity from Orbit-Flip Homoclinic Orbit of Weak Type ⋮ A THREE-DIMENSIONAL NONLINEAR SYSTEM WITH A SINGLE HETEROCLINIC TRAJECTORY

Cites Work

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• Bifurcation of a homoclinic orbit with a saddle-node equilibrium
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Bifurcations of heteroclinic loops
• Singular heteroclinic cycles
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• Problems in homoclinic bifurcation with higher dimensions
• A non-transverse homoclinic orbit to a saddle-node equilibrium
• Exponential trichotomy and heteroclinic bifurcations

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