Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909292850839552 |
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| author | Oliveira, Diego F. M. |
| author_facet | Oliveira, Diego F. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11254 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map Oliveira, Diego F. M. Chaotic Dynamics 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. |
| title | Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2408.11254 |