The non-transverse Shil'nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies

DOI10.1016/S0167-2789(98)00311-XzbMath0986.37041OpenAlexW2043129778WikidataQ126557095 ScholiaQ126557095MaRDI QIDQ1808282

Alejandro J. Rodríguez-Luis, Alan R. Champneys

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(98)00311-x

zbMATH Keywords

periodic orbitsnumerical continuationhomoclinic orbitsreversibilityAndronov-Hopf bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (17)

Analysis of a Shil'nikov type homoclinic bifurcation ⋮ Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point ⋮ Dynamics near nonhyperbolic fixed points or nontransverse homoclinic points ⋮ SOME RESULTS ON CHUA'S EQUATION NEAR A TRIPLE-ZERO LINEAR DEGENERACY ⋮ CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION ⋮ BI-SPIRALING HOMOCLINIC CURVES AROUND A T-POINT IN CHUA'S EQUATION ⋮ Analysis of the T-point-Hopf bifurcation ⋮ Subsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps ⋮ From steady solutions to chaotic flows in a Rayleigh-Bénard problem at moderate Rayleigh numbers ⋮ From trigger to phase waves and back again ⋮ ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ₂-SYMMETRY: APPLICATION TO CHUA'S EQUATION ⋮ On the complexity of periodic and nonperiodic behaviors of a hysteresis-based electronic oscillator ⋮ Complex dynamics in the 1:3 spatial resonance ⋮ Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations ⋮ Bifurcation sequences in the interaction of resonances in a model deriving from nonlinear rotordynamics: The zipper ⋮ Isolas, cusps and global bifurcations in an electronic oscillator

Uses Software

• AUTO
• HomCont

Cites Work

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