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arXiv · 2408.11254

Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map

Diego F. M. Oliveira
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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.

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Diego F. M. Oliveira. 2024-08-21. Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map. https://arxiv.org/abs/2408.11254

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