Benettin algorithm
E695942
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm in dynamical systems theory
ⓘ
method for computing Lyapunov exponents ⓘ numerical algorithm ⓘ |
| alternativeTo |
QR-decomposition Lyapunov methods
ⓘ
Wolf algorithm for Lyapunov exponents NERFINISHED ⓘ |
| appliesTo |
continuous-time dynamical systems
ⓘ
discrete-time dynamical systems ⓘ |
| assumes |
existence of Lyapunov exponents
ⓘ
smoothness of the dynamical system ⓘ |
| basedOn |
evolution of tangent vectors along trajectories
ⓘ
linearization of the flow around a trajectory ⓘ |
| canCompute | spectrum of Lyapunov exponents ⓘ |
| category | computational method in chaos analysis ⓘ |
| computes | maximal Lyapunov exponent ⓘ |
| developedBy | Giancarlo Benettin NERFINISHED ⓘ |
| field |
chaos theory
ⓘ
dynamical systems ⓘ nonlinear dynamics ⓘ |
| hasKeyStep |
accumulation of growth rates of perturbation norms
ⓘ
integration of the reference trajectory ⓘ periodic renormalization of perturbation vectors ⓘ simultaneous integration of perturbation vectors ⓘ |
| hasProperty |
iterative
ⓘ
numerically intensive ⓘ sensitive to integration accuracy ⓘ |
| involves |
logarithmic averaging of perturbation growth
ⓘ
long-time integration to reach asymptotic regime ⓘ |
| output | numerical estimates of Lyapunov exponents ⓘ |
| relatedTo |
Gram–Schmidt orthonormalization
NERFINISHED
ⓘ
Lyapunov characteristic exponents NERFINISHED ⓘ Oseledec multiplicative ergodic theorem NERFINISHED ⓘ QR-based Lyapunov exponent algorithms ⓘ |
| requires |
Gram–Schmidt orthonormalization for multiple exponents
ⓘ
choice of initial perturbation vectors ⓘ numerical integration of the system equations ⓘ |
| timePeriod | late 1970s ⓘ |
| usedFor |
characterizing chaos in dynamical systems
ⓘ
detecting sensitive dependence on initial conditions ⓘ estimating Lyapunov exponents ⓘ quantifying the rate of separation of nearby trajectories ⓘ |
| usedIn |
analysis of strange attractors
ⓘ
celestial mechanics ⓘ chaos detection in nonlinear dynamical systems ⓘ climate and atmospheric models ⓘ engineering control systems ⓘ study of Hamiltonian chaos ⓘ |
Referenced by (2)
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