Bifurcations of the Hénon map with additive bounded noise

Lamb, Jeroen SW; Rasmussen, Martin; Tey, Wei Hao

doi:10.48550/arXiv.2504.02776

File(s)

2504.02776v1.pdf (4.73 MB)

Preprint version

OA Location

https://arxiv.org/abs/2504.02776

Author(s)

Lamb, Jeroen SW

Rasmussen, Martin

Tey, Wei Hao

Type

preprint

Abstract

We numerically study bifurcations of attractors of the Hénon map with additive bounded noise with spherical reach. The bifurcations are analysed using a finitedimensional 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.

Date Issued

2025-04-03

Citation

arXiv, 2025

URI

https://hdl.handle.net/10044/1/124142

URL

http://arxiv.org/abs/2504.02776v1

DOI

10.48550/arXiv.2504.02776

Journal / Book Title

arXiv

Copyright Statement

Description

Preprint version

Identifier

http://arxiv.org/abs/2504.02776v1

Subjects

math.DS

math.OC

37C70, 37B25, 37H20