Arnold tongue
E1046814
concept in dynamical systems theory
feature of forced oscillatory systems
phenomenon in nonlinear dynamics
Arnold tongue is a concept in dynamical systems theory describing wedge-shaped regions in parameter space where oscillators become frequency-locked under periodic forcing.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
concept in dynamical systems theory
ⓘ
feature of forced oscillatory systems ⓘ phenomenon in nonlinear dynamics ⓘ |
| appearsInModel |
forced Stuart–Landau oscillator
ⓘ
forced van der Pol oscillator NERFINISHED ⓘ standard circle map ⓘ |
| characterizedBy |
integer frequency ratios between oscillator and forcing
ⓘ
phase-locked solutions ⓘ rational rotation numbers ⓘ |
| dependsOn |
forcing amplitude
ⓘ
forcing frequency ⓘ intrinsic frequency of the oscillator ⓘ |
| describes |
frequency locking of oscillators under periodic forcing
ⓘ
wedge-shaped regions in parameter space ⓘ |
| field |
dynamical systems
ⓘ
mathematical physics ⓘ nonlinear dynamics ⓘ |
| hasProperty |
boundaries correspond to loss of phase locking
ⓘ
each tongue corresponds to a specific rational frequency ratio p:q ⓘ tongue width typically increases with forcing amplitude ⓘ tongues can overlap at large forcing amplitudes ⓘ |
| hasShape |
tongue-like region in parameter space
ⓘ
wedge-shaped region ⓘ |
| mathematicalContext |
bifurcation theory
ⓘ
rotation theory of circle maps ⓘ torus maps and quasi-periodicity ⓘ |
| namedAfter | Vladimir Arnold NERFINISHED ⓘ |
| occursIn |
forced nonlinear oscillators
ⓘ
parameter space of driven oscillators ⓘ phase-locked regions of circle maps ⓘ phase-locked regions of the standard circle map ⓘ synchronization diagrams ⓘ |
| relatedTo |
Devil's staircase
NERFINISHED
ⓘ
circle map ⓘ frequency locking ⓘ mode locking ⓘ phase locking ⓘ resonance in nonlinear systems ⓘ synchronization ⓘ |
| usedIn |
analysis of phase-locked loops
ⓘ
analysis of synchronization in biological oscillators ⓘ analysis of synchronization in circadian rhythms ⓘ analysis of synchronization in electronic circuits ⓘ analysis of synchronization in laser systems ⓘ analysis of synchronization in neural oscillators ⓘ study of entrainment by periodic forcing ⓘ |
| visualizedAs |
regions in a two-parameter plane
ⓘ
tongue-like domains emanating from rational frequency ratios ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.