4 papers
Local Uniform Finite Cyclicity of the Semihyperbolic Hemicycle in Quadratic Systems
Haibo Lu
We prove local uniform finite cyclicity of the labelled hemicycle in a full neighborhood of its base field in the twelve-dimensional space of planar quadratic vector f…
Local maximal-canard threshold shifts under Runge--Kutta discretization: an observable-specific order condition
Haibo Lu
Near a planar fast--slow fold, a local maximal canard is selected by the parameter at which the attracting and repelling slow manifolds meet. We compare this threshold for a physic…
Neutral Returns at High-Order Grazing: Sharp Cyclicity, Physical Codimension, and Weighted Crossover
Haibo Lu
We study a neutral periodic orbit of a continuous two-field flow that is tangent to a switching seam while nearby orbits enter the second field. We separate the roles of two govern…
Neutral Entry--Exit Cycles with Quadratic Grazing: Uniform Return Reduction and Local Two-Parameter Bifurcations
Haibo Lu
We study planar continuous piecewise-smooth slow--fast return circuits in which an invariant-line entry--exit passage is followed by a separated quadratic grazing and the reference…