{"slug":"oip-node-c23-attractors-dynamical-systems","title":"Node C23: Attractors / Dynamical Systems","body":"# Node C23: Attractors / Dynamical Systems\n\nC23 — Attractors / Dynamical Systems\n{\n  \"id\": \"C23\",\n  \"claim\": \"Dynamical systems evolve toward characteristic limiting sets (attractors) in phase space; deterministic systems can be unpredictable (chaos), and different initial conditions can converge to the same attractor.\",\n  \"domain\": [\"celestial mechanics\", \"meteorology\", \"cardiology\", \"ecology\", \"economics\"],\n  \"pattern\": [\"attractor\", \"strange_attractor\", \"chaos\", \"deterministic_unpredictability\", \"basin_of_attraction\"],\n  \"mechanism\": \"An attractor is a closed subset of phase space toward which nearby trajectories converge. Fixed points: stable equilibria. Limit cycles: periodic oscillation. Strange attractors (Lorenz, Rossler): fractal sets with sensitive dependence on initial conditions (Lyapunov exponent > 0). Feigenbaum: period-doubling route to chaos has universal ratio δ = 4.669... independent of system details.\",\n  \"scale\": \"all scales\",\n  \"claim_tier\": \"T0/T1\",\n  \"sources\": [\n    \"Poincare, H. (1890). 'Sur le probleme des trois corps et les equations de la dynamique.' Acta Math., 13, 1-270.\",\n    \"Lorenz, E.N. (1963). 'Deterministic Nonperiodic Flow.' J. Atmos. Sci., 20(2), 130-141.\",\n    \"Feigenbaum, M.J. (1978). 'Quantitative Universality for a Class of Nonlinear Transformations.' J. Stat. Phys., 19, 25-52.\",\n    \"Thom, R. (1972). Stabilite structurelle et morphogenese. Benjamin. [Catastrophe theory.]\"\n  ],\n  \"dual\": \"Fixed-point stability only — a system with no complex attractors, converging only to simple equilibria.\",\n  \"falsifier\": \"N/A for the mathematical theorems. For the mapping to physical reality: a dynamical system whose long-term behavior does not settle into any identifiable attractor structure — pure transience with no recurrence statistics.\",\n  \"rival_frame\": \"Attractors are features of mathematical models, not of reality. The model converges; the system does not know it has an attractor. 'Strange attractors' are visualization artifacts of low-dimensional projections. Feigenbaum's universality applies only to unimodal maps — a narrow class of systems.\",\n  \"independence_check\": \"HIGH. Poincare (celestial mechanics, Paris, 1890) discovered chaos studying the three-body problem. Lorenz (meteorology, MIT, 1963) found strange attractors in atmospheric convection. Feigenbaum (mathematics, Los Alamos, 1978) discovered universality in iterative maps. Thom (topology, Bures-sur-Yvette, 1972) developed catastrophe theory from structural stability. Four fields, four countries, eight decades, same pattern: systems have characteristic long-term behaviors.\",\n  \"pattern_type\": \"mathematical\",\n  \"maps_to_axiom\": [\"A7\"]\n}\n\n---\n\n## Corpus map\n- Same node, other planes: [Encyclopedia C23](/a/convergence-encyclopedia-c23) · [Inventory invariant](/a/oip-invariant-17-317-attractors-dynamical-systems-chaos)\n- Edges touching C23: [convergence edge 10](/a/oip-convergence-edge-10)\n- Catalogue hub: [Public Article](/a/oip-convergence-public-article) · [Schema](/a/oip-convergence-schema)","register":"oip_protocol","tags":["philosophy","oip","convergence-catalogue","node","systems-theory"],"category":null,"style":{},"claims":[{"id":"c1","text":"Dynamical systems evolve toward characteristic limiting sets called attractors in phase space.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Core definition of the node topic."},{"id":"c2","text":"Deterministic systems can exhibit unpredictability known as chaos.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Key assertion linking determinism and chaos."},{"id":"c3","text":"Different initial conditions can converge to the same attractor.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines basins of attraction."},{"id":"c4","text":"An attractor is a closed subset of phase space toward which nearby trajectories converge.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Formal definition of attractor."},{"id":"c5","text":"Strange attractors are fractal sets with sensitive dependence on initial conditions indicated by Lyapunov exponent greater than zero.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"Defines strange attractors and chaos indicator."},{"id":"c6","text":"The period-doubling route to chaos has a universal ratio δ approximately 4.669 independent of system details.","section":"# Node C23: Attractors / Dynamical Systems","tier":"mechanistic","source_ids":[],"source_status":"unsourced","why_material":"States Feigenbaum universality."}],"sources":[],"prov":{"model":"Fable 5 (Claude Code)","action":"write"}}