Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map
Chaotic Dynamics
2024-08-22 v1
Abstract
This study examines the dynamical properties of the Ikeda map, with a focus on bifurcations and chaotic behavior. We investigate how variations in dissipation parameters influence the system, uncovering shrimp-shaped structures that represent intricate transitions between regular and chaotic dynamics. Key findings include the analysis of period-doubling bifurcations and the onset of chaos. We utilize Lyapunov exponents to distinguish between stable and chaotic regions. These insights contribute to a deeper understanding of nonlinear and chaotic dynamics in optical systems.
Keywords
Cite
@article{arxiv.2408.11254,
title = {Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map},
author = {Diego F. M. Oliveira},
journal= {arXiv preprint arXiv:2408.11254},
year = {2024}
}