Bifurcations of the H\'enon map with additive bounded noise
Dynamical Systems
2026-03-31 v2 Optimization and Control
Abstract
We numerically study bifurcations of attractors of the H\'enon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finite-dimensional boundary map. We distinguish between two types of bifurcations: topological bifurcations and boundary bifurcations. Topological bifurcations describe discontinuous changes of attractors and boundary bifurcations occur when singularities of an attractor's boundary are created or destroyed. We identify correspondences between topological and boundary bifurcations of attractors and local and global bifurcations of the boundary map.
Cite
@article{arxiv.2504.02776,
title = {Bifurcations of the H\'enon map with additive bounded noise},
author = {Jeroen S. W. Lamb and Martin Rasmussen and Wei Hao Tey},
journal= {arXiv preprint arXiv:2504.02776},
year = {2026}
}
Comments
26 pages, 17 figures