From the 2 of 4 linked papers with an AI index.
4 papers
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
The paper analyzes how many limit cycles can appear in planar slow–fast piecewise‑smooth systems when an invariant‑line entry‑exit delay and a quadratic grazing of the switching li…
Local Uniform Finite Cyclicity of the Semihyperbolic Hemicycle
Haibo Lu
The paper proves that, in a specific annular region of a compactified quadratic vector field, the number of isolated limit cycles is uniformly bounded for all small values of a fiv…