Lyapunov exponent
Trajectory divergence rate
A Lyapunov exponent measures how quickly nearby trajectories in a dynamical system diverge or converge over time.
A positive exponent indicates chaos—small differences in initial conditions grow exponentially, making long-term prediction impossible.
A negative exponent means trajectories converge toward stability.
The system's largest Lyapunov exponent determines whether it behaves chaotically.
Named for Russian mathematician Aleksandr Lyapunov.
Fractal pattern in chaos
- butterfly effectSmall inputs, disproportionate results
- sensitivityResponsiveness to stimuli
- initial conditionsState at time zero
- bifurcationDivision into two branches
fractals · nonlinearity · perturbation · deterministic chaos · turbulence · feedback loops
State of balance
- convergenceProcess of approaching sameness
- divergenceSeparation from common origin
- fixed pointValue unchanged by function
- dampingDissipation of vibrational energy
Continuous range of values
- embeddingPlacing within surrounding mass
- time delayPlanned interval before action
- QR decompositionMatrix as orthogonal-triangular product
strange attractor
Fractal pattern in chaos
- butterfly effectSmall inputs, disproportionate results
- sensitivityResponsiveness to stimuli
- initial conditionsState at time zero
bifurcation · fractals · nonlinearity · perturbation · deterministic chaos · turbulence · feedback loops
equilibrium
State of balance
- convergenceProcess of approaching sameness
- divergenceSeparation from common origin
- fixed pointValue unchanged by function
spectrum
Continuous range of values
- embeddingPlacing within surrounding mass
- time delayPlanned interval before action
- QR decompositionMatrix as orthogonal-triangular product
- stability theorystructural stability, instability, equilibrium, attractor, attractors
- Fractalsfractal, fractals, self-similar, Hausdorff dimension, recursion
Lyapunov exponents, exponent, exponential, exponentially, exponents, exponentiation