systems/standard_map.json

{
  "system_id": "standard_map",
  "name": "Standard map (Chirikov–Taylor map)",
  "category": "mixed",
  "equations": "p_{n+1} = p_n + K sin θ_n; θ_{n+1} = θ_n + p_{n+1} (mod 2π)",
  "parameters": {
    "K": 1.5
  },
  "description_simple": "A discrete map with both chaotic and regular regions in phase space.",
  "description_complex": "The standard map is a canonical area-preserving map that exhibits a mixed phase space: islands of stability coexist with a chaotic sea. For K ≈ 1.5, large chaotic regions form, but quasi-periodic invariant tori persist. This system is crucial for studying chaos onset, KAM theory, and reasoning about partial chaos.",
  "truth_assignment": {
    "Chaotic": true,
    "Deterministic": true,
    "PosLyap": true,
    "Sensitive": true,
    "StrangeAttr": false,
    "PointUnpredictable": true,
    "StatPredictable": true,
    "QuasiPeriodic": false,
    "Random": false,
    "FixedPointAttr": false,
    "Periodic": false,
    "Dissipative": false,
    "Bounded": true,
    "Mixing": true,
    "Ergodic": true,
    "HyperChaotic": false,
    "Conservative": true,
    "HighDimensional": false,
    "Multifractal": false,
    "HighDimSystem": false,
    "ContinuousTime": false,
    "DiscreteTime": true,
    "DelaySystem": false,
    "Forced": false,
    "Autonomous": true,
    "StrongMixing": true,
    "WeakMixing": true
  }
}