Effective drifts in dynamical systems with multiplicative noise: a review of recent progress

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dc.citation.epage053901-21en_US
dc.citation.issueNumber5en_US
dc.citation.spage053901-1en_US
dc.citation.volumeNumber79en_US
dc.contributor.authorVolpe, G.en_US
dc.contributor.authorWehr, J.en_US
dc.date.accessioned2018-04-12T10:45:10Z
dc.date.available2018-04-12T10:45:10Z
dc.date.issued2016en_US
dc.departmentInstitute of Materials Science and Nanotechnology (UNAM)en_US
dc.description.abstractNoisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system's state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental studies. Here, we provide an extensive review of the state of the art in this field. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment.en_US
dc.identifier.doi10.1088/0034-4885/79/5/053901en_US
dc.identifier.issn0034-4885
dc.identifier.urihttp://hdl.handle.net/11693/36585
dc.language.isoEnglishen_US
dc.publisherInstitute of Physics Publishingen_US
dc.relation.isversionofhttps://doi.org/10.1088/0034-4885/79/5/053901en_US
dc.source.titleReports on Progress in Physicsen_US
dc.subjectDelayed feedbacken_US
dc.subjectDynamical systemsen_US
dc.subjectEffective driftsen_US
dc.subjectMultiplicative noiseen_US
dc.subjectTime-scale competitionen_US
dc.titleEffective drifts in dynamical systems with multiplicative noise: a review of recent progressen_US
dc.typeArticleen_US
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