Bifurcations of the Hénon Map with Additive Bounded Noise
Abstract
Abstract. We numerically study bifurcations of attractors of the Hénon map with additive bounded noise with spherical reach. The bifurcations are analyzed 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.
Fields of Study & Subjects
Chaos control and synchronization
Quantum chaos and dynamical systems
stochastic dynamics and bifurcation
Publication details
- Journal / source
- SIAM Journal on Applied Dynamical Systems
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 25
- Issue
- 1
- Pages
- 351–374
- Publication date
- 28 January 2026
- Language
- EN