systems/logistic_r4.json

{
  "system_id": "logistic_r4",
  "name": "Logistic map (r = 4.0)",
  "category": "chaotic",
  "equations": "x_{n+1} = r x_n (1 - x_n)",
  "parameters": {
    "r": 4.0
  },
  "description_simple": "A discrete-time nonlinear map on the interval [0, 1] that shows chaotic behavior when the parameter r is 4.0.",
  "description_complex": "A one-dimensional, fully deterministic iterated map defined on [0, 1], where the update rule x_{n+1} = 4 x_n (1 - x_n) produces strong sensitivity to initial conditions, a positive Lyapunov exponent, and an invariant fractal measure. It is a standard textbook example of deterministic chaos.",
  "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
  }
}