# Nonlinear system
<!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside -->
## Microsims — p5.js
### Nonlinear system (p5.js) · `f(ax)≠af(x)`
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/1_JVzl6L5" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Nonlinear system — p5.js microsim"></iframe>
</div>
*A system that breaks linearity — capable of harmonics, limit cycles, and chaos.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/1_JVzl6L5) · movement *VI · Control theory & estimation* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree:
- [[Bifurcation_theory]] *(in tree)*
- [[Chaos_theory]] *(in tree)*
- [[Feedback]] *(in tree)*
- [[Graph_theory]] *(in tree)*
- [[Information_theory]] *(in tree)*
- [[Integral_transform]] *(in tree)*
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## MicroSim spec
- **Recommended sim type:** [[Dynamical_system|dynamical system]] / [[Phase_space|phase space]]
- **Microsimmability score:** 82/100
- **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below.
### Parameters (tunable controls)
- `Nonlinearity`
- `Input amplitude`
- `Damping`
### What animates
A nonlinear oscillator responds with thresholds, jumps, and harmonics as input grows.
### Learning objective
Contrast nonlinear responses with proportional linear behavior.
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Nonlinear_system.json (2026-07-30T02:09:12Z) -->
[[Adaptation]] · [[Agent-based_model]] · `Algebraic_Riccati_equation` · `Amplitude_death` · [[Ant_colony_optimization_algorithms]] · `Antilinear_map` · [[Artificial_intelligence]] · [[Artificial_life]] · [[Attractor]] · `Augustin-Louis_Cauchy` · `Autonomous_system_(mathematics)` · [[Autopoiesis]] · `Ball_and_beam` · `Bellman_equation` · [[Bifurcation_theory]] · `Biologist` · `Boltzmann_equation` · `Boundary_value_problem` · [[Bounded_rationality]] · `Carathéodory's_existence_theorem` · [[Cellular_automaton]] · [[Centrality]] · [[Chaos_theory]] · `Closed-form_expression` · [[Collective_action]] · [[Collective_behavior]] · [[Collective_consciousness]] · [[Collective_intelligence]] · [[Complex_adaptive_system]] · `Complex_number` · [[Complex_system]] · `Continuous_function` · [[Conversation_theory]] · [[Coupled_map_lattice]] · `Crank–Nicolson_method` · [[Cybernetics]] · `Daniel_Lazard` · `Delay_differential_equation` · `Dependent_and_independent_variables` · `Derivative` · `Diederich_Hinrichsen` · `Differentiable_function` · `Differential-algebraic_system_of_equations` · [[Differential_equation]] · `Differential_operator` · `Dirac_delta_function` · `Dirichlet_boundary_condition` · [[Dissipative_system]] · [[Dynamic_network_analysis]] · [[Dynamical_system]] · `Eduardo_D._Sontag` · `Elliptic_integral` · [[Emergence]] · `Engineer` · [[Entropy]] · `Equation` · `Ernst_Leonard_Lindelöf` · `Erwin_Kreyszig` · `Euler_method` · [[Evolution]] · [[Evolutionary_computation]] · [[Evolutionary_developmental_biology]] · [[Evolutionary_game_theory]] · [[Evolutionary_robotics]] · [[Evolvability]] · `Exact_differential_equation` · `Exponential_decay` · `Exponential_stability` · [[Feedback]] · `Finite_difference_method` · `Finite_element_method` · `Finite_volume_method` · [[Fluid_dynamics]] · [[Fractal]] · `Function_(mathematics)` · `Galerkin_method` · [[Game_theory]] · `General_relativity` · [[Genetic_algorithm]] · [[Genetic_programming]] · [[Geomorphology]] · `Ginzburg–Landau_theory` · [[Goal_orientation]] · `Gottfried_Wilhelm_Leibniz` · [[Graph_theory]] · `Gravity` · `Hamiltonian_system` · [[Herd_mentality]] · `Hofstadter_sequence` · `Holonomic_function` · [[Homeostasis]] · `Homogeneous_differential_equation` · `Homogeneous_function` · [[Information_theory]] · `Initial_condition` · `Integral` · [[Integral_transform]] · `Integrating_factor` · `Integration_by_substitution` · `Integro-differential_equation` · [[Isaac_Newton]] · `Ishimori_equation` · `Jacob_Bernoulli` · `Jet_bundle` · `John_Crank` · `Joseph-Louis_Lagrange` · `Józef_Maria_Hoene-Wroński` · `Kadomtsev–Petviashvili_equation` · `Lagrangian_mechanics` · `Landau–Lifshitz–Gilbert_equation` · `Leonhard_Euler` · `Limit_cycle` · `Linear_combination` · `Linear_differential_equation` · `Linear_equation` · `Linear_map` · `Linear_system` · `Linearization` · `List_of_linear_ordinary_differential_equations` · `List_of_named_differential_equations` · `List_of_nonlinear_ordinary_differential_equations` · `List_of_nonlinear_partial_differential_equations` · `Liénard_equation` · `Logistic_map` · `Lotka–Volterra_equations` · `Lyapunov_function` · [[Lyapunov_stability]] · `MATLAB` · [[Machine_learning]] · `Map_(mathematics)` · `Martin_Kutta` · `Mathematician` · `Mathematics` · `Method_of_characteristics` · `Method_of_undetermined_coefficients` · `Mode_coupling` · [[Multistability]] · `Navier–Stokes_equations` · [[Network_motif]] · [[Network_science]] · [[Neural_network_(machine_learning)]] · `Newton's_method` · `Nonelementary_integral` · `Nonlinear_Dynamics_(journal)` · `Nonlinear_Schrödinger_equation` · `Nonlinear_optics` · `Nonlinear_partial_differential_equation` · `Nonlinear_system_identification` · `Nonlinearity_(disambiguation)` · `Notation_for_differentiation` · [[Numerical_integration]] · [[Operationalization]] · [[Ordinary_differential_equation]] · [[Partial_differential_equation]] · [[Particle_swarm_optimization]] · [[Pattern_formation]] · `Peano_existence_theorem` · [[Percolation]] · `Percolation_theory` · `Perturbation_theory` · `Phase_portrait` · [[Phase_space]] · [[Phase_transition]] · `Phyllis_Nicolson` · `Physicist` · `Picard–Lindelöf_theorem` · `Polynomial` · [[Population_dynamics]] · `Power-flow_study` · `Power_series_solution_of_differential_equations` · [[Prisoner's_dilemma]] · `Proportionality_(mathematics)` · `Randomness` · `Rate_of_convergence` · [[Rational_choice_model]] · `Rational_number` · [[Reaction–diffusion_system]] · `Real-root_isolation` · `Real_number` · [[Recurrence_relation]] · `Richards_equation` · [[Robustness_(computer_science)]] · `Root-finding_algorithm` · `Rudolf_Lipschitz` · `Runge–Kutta_methods` · [[Scalability]] · [[Scale-free_network]] · `Scale_analysis_(mathematics)` · [[Science]] · `Scientist` · [[Second-order_cybernetics]] · [[Self-organization]] · [[Self-organized_criticality]] · `Self-oscillation` · [[Self-reference]] · [[Self-replication]] · [[Sensemaking]] · `Separation_of_variables` · [[Sequence]] · `Sine-Gordon_equation` · [[Small-world_network]] · [[Social_dynamics]] · [[Social_network_analysis]] · `Sofya_Kovalevskaya` · `Soliton` · [[Spatial_ecology]] · `Stanisław_Ulam` · `Stochastic_differential_equation` · `Stochastic_partial_differential_equation` · `Superposition_principle` · [[Swarm_behaviour]] · [[Synchronization]] · [[System]] · [[System_dynamics]] · `System_of_linear_equations` · [[Systems_biology]] · [[Systems_science]] · [[Systems_theory]] · [[Systems_thinking]] · `Theory_of_computation` · [[Time_series]] · `Van_der_Pol_oscillator` · `Variable_(mathematics)` · `Variation_of_parameters` · [[Variety_(cybernetics)]] · `Vector_soliton` · `Vlasov_equation` · `Volterra_series` · [[Wayback_Machine]] · `Wronskian` · `Émile_Picard`
## From the Real GENERATIVE library
*Nonlinear system — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (STEM and Music room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:PendulumLayout.svg).*
> Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour ([Wikipedia](https://en.wikipedia.org/wiki/Nonlinear_system))
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## From the vault media library
!Nonlinear system thumb.png
*Nonlinear System — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*
<!-- LOCAL-MEDIA-PASS:END -->
> p5.js MicroSim stub · part of Systems Science · [Wikipedia source](https://en.wikipedia.org/wiki/Nonlinear_system)
> Relation: subfield of systems science.
## Concept summary
A nonlinear system is one whose output is not proportional to its input, giving rise to rich behavior such as thresholds, oscillations, and chaos.
## Build checklist
- [ ] Claim it: set `status: in-progress` + `lease` + `leased_at`
- [ ] Write the child page explaining the concept (tie it back to systems science)
- [ ] 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: Nonlinear system
let controls = {};
function setup() {
// createCanvas(...); create sliders for the parameters above.
}
function draw() {
// background(...); read controls; render dynamical system / phase space; respond live.
}
```
---
Back to Systems Science · Wikipedia: [Nonlinear system](https://en.wikipedia.org/wiki/Nonlinear_system)
---
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## 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 (8):** 🟡 system (24) · 🟢 attractor chaos (5) · 🟡 science (5) · 🟢 oscillation (2) · 🟢 threshold (2) · 🟢 amplitude (1) · 🟢 damping (1) · 🟢 harmonic (1)
**Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Nonlinear_system) : [Wikitube](https://en.wikitube.io/wiki/Nonlinear_system)
## Previous hub tags
Tree parents: [[Complex_system]] · [[Control_theory]] · [[Cybernetics]] · [[Dynamical_system]] · [[Emergence]] · [[Feedback]] · [[Phase_space]] · [[Self-organization]] · [[System_dynamics]] · [[Systems_science]] · [[Systems_theory]].
Legacy hubs: none.
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*Sources: 2 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*