Open access
Date
2022-12Type
- Journal Article
Abstract
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the Jacobian matrix of the mapping. In this work, a detailed analysis of the transformation rules for Langevin equations under general nonlinear mappings is presented. We show how to identify systems with exact potentials by understanding their differential-geometric properties. To demonstrate the power of our method, we use it to derive exact potentials for broadly studied models of nonlinear deterministic and stochastic oscillations. In selected examples, we visualize the identified potentials. Our results imply a broad class of exactly solvable stochastic models, which can be self-consistently defined from given deterministic gradient systems. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000589449Publication status
publishedExternal links
Journal / series
ChaosVolume
Pages / Article No.
Publisher
American Institute of PhysicsSubject
stochastic dynamical systemsOrganisational unit
09471 - Noiray, Nicolas / Noiray, Nicolas
Funding
184617 - Thermoakustische Instabilitäten in Rohr-Ringbrennkammern (SNF)
Related publications and datasets
Is part of: https://doi.org/10.3929/ethz-b-000664067
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