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Updated: Jun 7, 2026

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Mapping chaos: Bifurcation patterns and shrimp structures in the Ikeda map
1School of Electrical Engineering and Computer Science, College of Engineering & Mines, University of North Dakota, Grand Forks, North Dakota 58202-8367, USA.
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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