Linearly independent homoclinic bifurcations parameterized by a small function

DOI10.1016/j.jde.2007.05.017zbMath1138.34024OpenAlexW2052199806MaRDI QIDQ996238

Chang Rong Zhu, Wei Nian Zhang

Publication date: 13 September 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.05.017

zbMATH Keywords

codimensionLyapunov-Schmidt reductionlinear independencedegenerate homoclinic bifurcationbifurcation manifold

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (9)

Homoclinic finger-rings in \(\mathbb{R}^N\) ⋮ Admissibility and nonuniform exponential dichotomies ⋮ Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation ⋮ Multiple families of bounded solutions near perturbed homoclinic orbits, application to a nonlinear wave equation ⋮ Periodic solutions and homoclinic bifurcation of a predator-prey system with two types of harvesting ⋮ Computation of bifurcation manifolds of linearly independent homoclinic orbits ⋮ Multiple homoclinic solutions for singular differential equations ⋮ The transversal homoclinic solutions and chaos for stochastic ordinary differential equations ⋮ Multiple chaos arising from single-parametric perturbation of a degenerate homoclinic orbit

Cites Work

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• Bifurcation of homoclinics in a nonlinear oscillation
• Perturbation of homoclinics and subharmonics in duffing's equation
• Transverse homoclinic orbits in periodically perturbed parabolic equations
• Bifurcation from a homoclinic orbit in parabolic differential equations
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension
• Bounded solutions for non-autonomous parabolic equations

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