An asymptotic solution slowly crossing the separatrix near a saddle centre bifurcation point

DOI10.1088/0951-7715/16/1/320zbMath1026.34062OpenAlexW2013538713MaRDI QIDQ4801893

S. G. Glebov, Oleg M. Kiselev

Publication date: 2 December 2003

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/16/1/320

zbMATH Keywords

asymptotic solutionsaddle-centre bifurcationprimary resonance equation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Qualitative investigation and simulation of ordinary differential equation models (34C60) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

The capture into parametric autoresonance ⋮ The capture of a particle into resonance at potential hole with dissipative perturbation ⋮ An asymptotic structure of the bifurcation boundary of the perturbed Painlevé-2 equation ⋮ Adiabatic approximation for a model of cyclotron motion ⋮ Jump of the adiabatic invariant at a separatrix crossing: degenerate cases ⋮ Conditions for Phase Locking and Dephasing of Autoresonant Pumping ⋮ Oscillations near a separatrix in the Duffing equation ⋮ Adiabatic approximation in a resonance capture problem ⋮ Capture and holding of resonance far from equilibrium ⋮ Scattering of trajectories at a separatrix under autoresonance ⋮ Averaging method for systems with separatrix crossing ⋮ Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet ⋮ Jumps of adiabatic invariant at the separatrix of a degenerate saddle point

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