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

TL;DR

This paper explores the bifurcation patterns and chaotic structures in the Ikeda map, revealing intricate transitions and the influence of dissipation parameters on system dynamics, with implications for nonlinear optical systems.

Contribution

It uncovers shrimp-shaped structures and analyzes bifurcation sequences in the Ikeda map, advancing understanding of chaos in nonlinear optical systems.

Findings

Identification of shrimp-shaped structures in bifurcation diagrams

Analysis of period-doubling routes to chaos

Lyapunov exponent mapping of stable and chaotic regions

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.