Lorenz attractor
E620668
The Lorenz attractor is a famous chaotic set arising from a simplified model of atmospheric convection, known for its butterfly-shaped trajectory and role as an early example of deterministic chaos in dynamical systems.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Lorenz attractor canonical | 3 |
| Lorenz system | 2 |
| Lorenz equations | 1 |
| Lorenz system of differential equations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6801245 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Lorenz attractor Context triple: [Poincaré–Bendixson theorem, contrastsWith, Lorenz attractor]
-
A.
Lorenz
Lorenz is a masculine given name of German origin, historically borne by various notable figures in Europe.
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B.
Lyapunov fractal
The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
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C.
Smale horseshoe
The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
-
D.
Zhabotinsky
Zhabotinsky is a Russian surname most notably associated with Vladimir Yevgenyevich Zhabotinsky, a prominent Soviet chemist known for his work on nonlinear chemical oscillations and the Belousov–Zhabotinsky reaction.
-
E.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Lorenz attractor Target entity description: The Lorenz attractor is a famous chaotic set arising from a simplified model of atmospheric convection, known for its butterfly-shaped trajectory and role as an early example of deterministic chaos in dynamical systems.
-
A.
Lorenz
Lorenz is a masculine given name of German origin, historically borne by various notable figures in Europe.
-
B.
Lyapunov fractal
The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
-
C.
Smale horseshoe
The Smale horseshoe is a fundamental example in dynamical systems theory that illustrates chaotic behavior through a specific stretching-and-folding map of a square into a horseshoe-shaped region.
-
D.
Zhabotinsky
Zhabotinsky is a Russian surname most notably associated with Vladimir Yevgenyevich Zhabotinsky, a prominent Soviet chemist known for his work on nonlinear chemical oscillations and the Belousov–Zhabotinsky reaction.
-
E.
Lyapunov exponents
Lyapunov exponents are quantitative measures in dynamical systems theory that characterize the rates at which nearby trajectories diverge or converge, indicating the presence and strength of chaos.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
chaotic attractor
ⓘ
dynamical system object ⓘ mathematical object ⓘ strange attractor ⓘ |
| arisesFrom |
Lorenz system of differential equations
ⓘ
linked to:
Lorenz attractor
simplified model of atmospheric convection ⓘ |
| associatedWith |
paper "Deterministic Nonperiodic Flow"
ⓘ
linked to:
Deterministic Nonperiodic Flow
|
| category |
attractors in phase space
ⓘ
chaotic dynamical systems ⓘ nonlinear dynamical systems ⓘ |
| coordinateVariables |
x
ⓘ
y ⓘ z ⓘ |
| definedIn | three-dimensional phase space ⓘ |
| describes | asymptotic behavior of the Lorenz system ⓘ |
| equationSystem |
dx/dt = σ (y − x)
ⓘ
dy/dt = x (ρ − z) − y ⓘ dz/dt = x y − β z ⓘ |
| field |
applied mathematics
ⓘ
chaos theory ⓘ dynamical systems ⓘ meteorology ⓘ nonlinear dynamics ⓘ |
| hasDimension | fractal dimension between 2 and 3 ⓘ |
| hasProperty |
bounded trajectories
ⓘ
dense set of periodic orbits ⓘ deterministic chaos ⓘ non-integrable system behavior ⓘ non-periodic trajectories ⓘ sensitive dependence on initial conditions ⓘ strange attractor with fractal structure ⓘ structural instability with respect to parameters ⓘ topologically mixing ⓘ |
| hasShape | butterfly-shaped trajectory in phase space ⓘ |
| influenced | development of modern chaos theory ⓘ |
| introducedBy | Edward N. Lorenz ⓘ |
| namedAfter | Edward N. Lorenz ⓘ |
| publicationYear | 1963 ⓘ |
| publishedIn | Journal of the Atmospheric Sciences ⓘ |
| relatedConcept |
butterfly effect
ⓘ
chaotic flow ⓘ strange attractor ⓘ |
| typicalParameterBeta | 8/3 ⓘ |
| typicalParameterRho | 28 ⓘ |
| typicalParameterSigma | 10 ⓘ |
| usedAs |
benchmark system in chaos theory
ⓘ
canonical example of deterministic chaos ⓘ |
| visualizedBy |
Poincaré sections
ⓘ
linked to:
Poincaré map
phase-space trajectory plots ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Lorenz attractor Description of subject: The Lorenz attractor is a famous chaotic set arising from a simplified model of atmospheric convection, known for its butterfly-shaped trajectory and role as an early example of deterministic chaos in dynamical systems.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lorenz attractor
linked to: Lorenz attractor
linked to: Lorenz attractor
linked to: Lorenz attractor