chaos theory
E577499
Chaos theory is a branch of mathematics and physics that studies how small differences in initial conditions can lead to vastly different outcomes in complex, dynamical systems, making long-term prediction effectively impossible.
Statements (63)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematics
ⓘ
branch of physics ⓘ mathematical theory ⓘ theory of dynamical systems ⓘ |
| appliesTo |
celestial mechanics
ⓘ
chemical reactions ⓘ ecological systems ⓘ economics and financial markets ⓘ electrical circuits ⓘ mechanical oscillators ⓘ neural activity ⓘ population dynamics ⓘ turbulent fluid flow ⓘ weather systems ⓘ |
| coreExample |
Henon map
NERFINISHED
ⓘ
Lorenz system NERFINISHED ⓘ Rössler attractor NERFINISHED ⓘ double pendulum ⓘ logistic map NERFINISHED ⓘ |
| developedFrom |
dynamical systems theory
ⓘ
nonlinear differential equations ⓘ |
| emergedIn | 20th century ⓘ |
| fieldOfStudy |
deterministic chaos
ⓘ
nonlinear dynamics ⓘ sensitive dependence on initial conditions ⓘ |
| hasKeyConcept |
Lyapunov exponent
NERFINISHED
ⓘ
bifurcation diagram ⓘ butterfly effect ⓘ dense periodic orbits ⓘ fractal dimension ⓘ logistic map ⓘ sensitive dependence on initial conditions ⓘ strange attractor ⓘ topological mixing ⓘ |
| hasPioneer |
Benoit Mandelbrot
NERFINISHED
ⓘ
Edward Lorenz NERFINISHED ⓘ Henri Poincaré NERFINISHED ⓘ Mitchell Feigenbaum NERFINISHED ⓘ Stephen Smale NERFINISHED ⓘ |
| hasProperty |
aperiodic
ⓘ
deterministic ⓘ highly sensitive to initial conditions ⓘ long-term unpredictability ⓘ |
| relatedTo |
complex systems
ⓘ
control theory ⓘ ergodic theory ⓘ fractal geometry ⓘ information theory NERFINISHED ⓘ nonlinear dynamics ⓘ statistical mechanics ⓘ |
| studies |
bifurcations
ⓘ
deterministic yet unpredictable behavior ⓘ dynamical systems ⓘ fractal structures in phase space ⓘ long-term unpredictability ⓘ nonlinear systems ⓘ sensitivity to initial conditions ⓘ strange attractors ⓘ |
| usesTool |
Lyapunov exponents
NERFINISHED
ⓘ
Poincaré maps NERFINISHED ⓘ bifurcation analysis ⓘ numerical simulation ⓘ phase space analysis ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.