systems/ikeda_map.json

{
  "system_id": "ikeda_map",
  "name": "Ikeda map",
  "category": "chaotic",
  "equations": "x_{n+1} = 1 + u (x_n cos t_n - y_n sin t_n); y_{n+1} = u (x_n sin t_n + y_n cos t_n); t_n = 0.4 - 6/(1 + x_n^2 + y_n^2)",
  "parameters": {
    "u": 0.9
  },
  "description_simple": "A nonlinear map modeling the behavior of light in an optical cavity, exhibiting chaotic dynamics.",
  "description_complex": "The Ikeda map describes the evolution of a light beam reflecting inside an optical cavity with nonlinear refractive index. The map produces a chaotic attractor with strong sensitivity to initial conditions, a positive Lyapunov exponent, fractal basin boundaries, and deterministic chaos emerging from optical physics.",
  "truth_assignment": {
    "Chaotic": true,
    "Deterministic": true,
    "PosLyap": true,
    "Sensitive": true,
    "StrangeAttr": true,
    "PointUnpredictable": true,
    "StatPredictable": true,
    "QuasiPeriodic": false,
    "Random": false,
    "FixedPointAttr": false,
    "Periodic": false,
    "Dissipative": true,
    "Bounded": true,
    "Mixing": true,
    "Ergodic": true,
    "HyperChaotic": false,
    "Conservative": false,
    "HighDimensional": false,
    "Multifractal": false,
    "HighDimSystem": false,
    "ContinuousTime": false,
    "DiscreteTime": true,
    "DelaySystem": false,
    "Forced": false,
    "Autonomous": true,
    "StrongMixing": true,
    "WeakMixing": true
  }
}