nonlinearities
Deviations from proportionality
Nonlinearities are instances where effects don't scale proportionally with causes.
In linear systems, doubling the input doubles the output; nonlinearities break this pattern.
The term appears in physics, engineering, economics, and statistics to describe behaviors that can't be captured by straight-line relationships: The model failed to account for nonlinearities in the data.
Nonlinearities often produce unexpected outcomes—threshold effects, feedback loops, or chaotic dynamics.
Increase in intensity
- saturationState of complete permeation
- distortionTwisting from original state
- gainPositive return received
- oscillationRepeated back-and-forth movement
runaway · stabilization · attenuation · hysteresis · threshold · clipping · compression · positive feedback
Repeated back-and-forth movement
- bifurcationDivision into two branches
- amplitudeMaximum oscillation displacement
- harmonicOf musical overtones
- resonanceAmplified oscillation at natural frequency
damping · hysteresis · saturation · steady-state · transient · equilibrium · coupling · perturbation
Small inputs, disproportionate results
- strange attractorFractal pattern in chaos
- bifurcationDivision into two branches
- fractalsPatterns repeating at every scale
- sensitivityResponsiveness to stimuli
initial conditions · unpredictability · deterministic chaos · cascade · turbulence · emergence · self-organization · complexity
Expression with variable terms
- exponentialIncreasing by constant ratio
- logarithmicBased on exponents
- quadraticInvolving squared terms
- cubicOf three dimensions
sigmoid · power law · asymptote · discontinuity · inflection point · curvature · Taylor expansion · approximation
Twisting from original state
- asymmetryAbsence of balanced form
- fluctuationsIrregular rises and falls
- anomaliesDepartures from expected patterns
- heterogeneityState of being dissimilar
unevenness · variability · skewness · deviation · aberration · discontinuity · unpredictability · disproportionality
amplification
Increase in intensity
- saturationState of complete permeation
- distortionTwisting from original state
- gainPositive return received
oscillation · runaway · stabilization · attenuation · hysteresis · threshold · clipping · compression · positive feedback · negative feedback
oscillation
Repeated back-and-forth movement
- bifurcationDivision into two branches
- amplitudeMaximum oscillation displacement
- harmonicOf musical overtones
resonance · damping · hysteresis · saturation · steady-state · transient · equilibrium · coupling · perturbation · elasticity
butterfly effect
Small inputs, disproportionate results
- strange attractorFractal pattern in chaos
- bifurcationDivision into two branches
- fractalsPatterns repeating at every scale
sensitivity · initial conditions · unpredictability · deterministic chaos · cascade · turbulence · emergence · self-organization · complexity · perturbation
polynomial
Expression with variable terms
- exponentialIncreasing by constant ratio
- logarithmicBased on exponents
- quadraticInvolving squared terms
cubic · sigmoid · power law · asymptote · discontinuity · inflection point · curvature · Taylor expansion · approximation · linearization
distortion
Twisting from original state
- asymmetryAbsence of balanced form
- fluctuationsIrregular rises and falls
- anomaliesDepartures from expected patterns
heterogeneity · unevenness · variability · skewness · deviation · aberration · discontinuity · unpredictability · disproportionality
nonlinearitieslinearities
States of being straight
proportionality · linear functions · linear equations · linearity · superposition
nonlinearitiesstability
Resistance to displacement
simplicity · predictability · additivity · superposition · regularity
line, lineage, alignment, linear, aligned, delineate, realignment, lineal, aligns