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.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
chaotic attractor
ⓘ
dynamical system object ⓘ mathematical object ⓘ strange attractor ⓘ |
| arisesFrom |
Lorenz system of differential equations
NERFINISHED
ⓘ
simplified model of atmospheric convection ⓘ |
| associatedWith | paper "Deterministic Nonperiodic Flow" NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| namedAfter | Edward N. Lorenz NERFINISHED ⓘ |
| publicationYear | 1963 ⓘ |
| publishedIn | Journal of the Atmospheric Sciences NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
phase-space trajectory plots ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.