Dynamical_systems_theory

# Dynamical systems theory ## MicroSim spec - **Recommended sim type:** [[Phase_space|phase space]] / [[Attractor|attractor]] - **Microsimmability score:** 87/100 - **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below. ### Parameters (tunable controls) - `Parameter a` - `Time step` - `Initial condition` ### What animates Trajectories sweep through state space toward fixed points or cycles as parameters change. ### Learning objective Show how trajectories in state space reveal a [[System|system]]'s long-term behavior. ## Links (Wikipedia order)  `A-not-B_error` · `Abstract_algebra` · `Affine_geometry` · `Algebra` · `Algebraic_geometry` · `Algebraic_number_theory` · `Algebraic_topology` · `Analytic_geometry` · `Analytic_number_theory` · `Analytical_mechanics` · `Andrey_Kolmogorov` · `Applied_mathematics` · `Arithmetic` · `Arithmetic_dynamics` · `Arithmetic_geometry` · [[Artificial_life]] · `Baker's_map` · `Biological_applications_of_bifurcation_theory` · `Biology` · `Butterfly_effect` · [[Calculus]] · [[Calculus_of_variations]] · `Cantor_set` · `Category_theory` · `Cell_(biology)` · [[Chaos_theory]] · [[Chemistry]] · `Classical_mechanics` · `Cognition` · [[Cognitive_science]] · `Combinatorics` · `Combinatorics_and_dynamical_systems` · `Commutative_algebra` · [[Complex_analysis]] · `Complex_geometry` · `Complex_plane` · [[Complexity]] · `Computational_complexity_theory` · `Computational_geometry` · `Computational_mathematics` · `Computer` · `Computer_algebra` · [[Computer_science]] · `Connectionism` · [[Control_theory]] · `Convex_geometry` · `David_Luenberger` · `Deterministic_system_(philosophy)` · `Developmental_psychology` · `Developmental_robotics` · `Diane_Larsen-Freeman` · [[Differential_equation]] · `Differential_geometry` · `Differential_topology` · `Diophantine_geometry` · `Discrete_geometry` · `Discrete_mathematics` · `Dmitri_Anosov` · [[Dynamical_system]] · `Dynamicism` · `Economics` · `Electronic_circuit` · `Elementary_algebra` · `Elon_Lindenstrauss` · [[Engineering]] · [[Engineering_mathematics]] · `Equations_of_motion` · `Ergodic_theory` · `Euclidean_geometry` · `Euler–Lagrange_equation` · [[Evolutionary_computation]] · [[Evolutionary_robotics]] · [[Feedback]] · `Field_(mathematics)` · `Finite_geometry` · `Flow_(mathematics)` · [[Formal_system]] · `Foundations_of_mathematics` · `Fourier_transform` · `Function_(mathematics)` · `Functional_(mathematics)` · [[Functional_analysis]] · `Future_of_mathematics` · [[Game_theory]] · `General_topology` · `Geometric_topology` · [[Geometry]] · `Gingerbreadman_map` · `Glossary_of_mathematical_symbols` · `Graph_dynamical_system` · [[Graph_theory]] · `Grigory_Margulis` · `Group_theory` · `Halo_orbit` · `Harmonic_analysis` · `Hillel_Furstenberg` · `History_of_mathematics` · `Homogeneity_(physics)` · `Homological_algebra` · `Homotopy_theory` · `Informal_mathematics` · `Information_geometry` · [[Information_theory]] · `Invariant_measure` · `Iterated_function` · `Jürgen_Moser` · `Language_attrition` · `Large_numbers` · [[Linear_algebra]] · `Linear_system` · `List_of_films_about_mathematicians` · `List_of_types_of_systems_theory` · `Lists_of_mathematics_topics` · `Lorenz_system` · `Manifold` · `Mathematical_analysis` · `Mathematical_and_theoretical_biology` · `Mathematical_chemistry` · `Mathematical_economics` · `Mathematical_finance` · `Mathematical_linguistics` · `Mathematical_logic` · [[Mathematical_model]] · [[Mathematical_optimization]] · `Mathematical_physics` · `Mathematical_psychology` · `Mathematical_sociology` · `Mathematical_statistics` · `Mathematics` · `Mathematics_and_art` · `Mathematics_education` · `Measure_(mathematics)` · `Mechanics` · `Meteorology` · `Michael_A._Arbib` · `Molecular_biology` · `Nature` · `Nikolay_Bogolyubov` · [[Nonlinear_system]] · `Number` · `Number_theory` · `Numerical_analysis` · [[Operations_research]] · `Operator_(mathematics)` · [[Oscillation]] · `Otomar_Hájek` · `Philosophy_of_mathematics` · [[Physics]] · `Point_(geometry)` · `Polynomial` · `Postcognitivism` · `Probability_theory` · [[Projective_geometry]] · `Psychology` · `Ralph_Abraham_(mathematician)` · `Randomness` · `Rational_function` · `Real_analysis` · `Recreational_mathematics` · `Recurrent_neural_network` · [[Science]] · [[Science_(journal)]] · `Scientific_modelling` · [[Self-organization]] · [[Sequence]] · `Set_(mathematics)` · [[Set_theory]] · `Sharkovskii's_theorem` · `Shift_operator` · `Simulation` · [[Society]] · `Sports_biomechanics` · `Statistics` · `Stefan_Banach` · `Stephen_Smale` · `Steven_Strogatz` · `Stochastic_differential_equation` · [[Stock_and_flow]] · `Superposition_principle` · `Symbolic_dynamics` · `Synergetics_(Haken)` · [[System]] · [[System_dynamics]] · `Systemography` · [[Systems_science]] · `Theory_of_computation` · `Tim_van_Gelder` · `Time` · `Timeline_of_mathematics` · `Topological_dynamics` · `Topology` · `Type_theory` · `Vector_space` · `Vito_Volterra` · `Vladimir_Arnold` · [[Wayback_Machine]] > p5.js MicroSim stub · part of Systems Thinking · [Wikipedia source](https://en.wikipedia.org/wiki/Dynamical_systems_theory) > Relation: subfield of systems thinking. ## Concept summary Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations by nature of the ergodicity of dynamic systems. When differential equations are employed, the theory is called continuous dynamical systems. ## Build checklist - [ ] Claim it: set `status: in-progress` + `lease` + `leased_at` - [ ] Write the child page explaining the concept (tie it back to systems thinking) - [ ] Finalize parameter ranges and defaults - [ ] Implement the p5.js sketch (drawing + control regions) - [ ] Add caption + the learning objective on the page - [ ] Set `status: done` ## p5.js sketch ```javascript // MicroSim: Dynamical systems theory let controls = {}; function setup() { // createCanvas(...); create sliders for the parameters above. } function draw() { // background(...); read controls; render phase space / attractor; respond live. } ``` --- Back to Systems Thinking · Wikipedia: [Dynamical systems theory](https://en.wikipedia.org/wiki/Dynamical_systems_theory) ---  ## Semiotic profile > *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.* **Universals (7):** 🟡 system (32) · 🟡 science (5) · 🟢 attractor chaos (4) · 🟢 state (3) · 🟢 cycle (2) · 🟢 damping (1) · 🟢 flow (1) **Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Dynamical_systems_theory) : [Wikitube](https://en.wikitube.io/wiki/Dynamical_systems_theory) ## Previous hub tags Tree parents: [[Complex_system]] · [[Control_theory]] · [[Dynamical_system]] · [[System_dynamics]] · [[Systems_science]] · [[Systems_theory]]. Legacy hubs: none. --- *Sources: 2 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*