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Novel patterns in discrete Ikeda map: Quint points and complex non-quantum chirality.

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This study details stable phases in the Ikeda map using stability diagrams. New non-quantum chiral structures and "shrimp islands" were discovered, enhancing understanding of complex system dynamics.

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Area of Science:

  • Dynamical systems theory
  • Nonlinear dynamics
  • Complex systems analysis

Background:

  • The Ikeda map is a well-known discrete dynamical system exhibiting complex behavior.
  • Understanding the distribution and patterns of stable phases is crucial for characterizing system dynamics.

Purpose of the Study:

  • To comprehensively investigate the distribution of stable phases in the discrete Ikeda map.
  • To identify and characterize novel structures and phenomena within the Ikeda map's phase space.

Main Methods:

  • Detailed analysis of stable phase distribution.
  • Utilization of three complementary stability diagrams: Lyapunov, isoperiod, and isospike.
  • Exploration of initial value perturbation effects on system topology.

Main Results:

  • Discovery of the adding-doubling complexification cascade.
  • Identification of novel non-quantum chiral pairs and complex chiral formations.
  • Observation of numerous hidden
  • shrimp islands
  • emerging from initial value perturbations in near-conservative states.

Conclusions:

  • The study enhances the understanding of non-quantum chiral structures in discrete dynamical systems.
  • New insights into stability and multistability within complex mappings have been provided.
  • The findings offer a deeper appreciation of the intricate dynamics of the Ikeda map.