Dissipative systems with nonlocal delayed feedback control

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dc.contributor.authorGrawitter, Josua
dc.contributor.authorvan Buel, Reinier
dc.contributor.authorSchaaf, Christian
dc.contributor.authorStark, Holger
dc.date.accessioned2018-11-26T12:22:20Z
dc.date.available2018-11-26T12:22:20Z
dc.date.issued2018-11-07
dc.description.abstractWe present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a nonzero system delay acts to destabilize the otherwise stable fixed point for sufficiently large feedback strengths. The imaginary part of the dominant eigenvalue is bounded by twice the feedback strength. In the relevant parameter space it changes discontinuously along specific lines when switching between eigenvalues. When the feedback control force is bounded by a sigmoid function, a supercritical Hopf bifurcation occurs at the stability–instability transition. Perturbing the fixed point, the frequency and amplitude of the resulting limit cycles respond to parameter changes like the dominant eigenvalue. In particular, they show similar discontinuities along specific lines. These results are largely independent of the exact shape of the sigmoid function. Our findings match well with previously reported results on a feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid (Zeitz et al 2015 Eur. Phys. J. E 38 22). Thus, our model captures the essential features of nonlocal delayed feedback control in spatially extended dissipative systems.en
dc.description.sponsorshipDFG, 325093850, Open Access Publizieren 2017 - 2018 / Technische Universität Berlinde
dc.identifier.eissn1367-2630
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/8569
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-7703
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/en
dc.subject.ddc530 Physikde
dc.subject.othertime-delayed feedbacken
dc.subject.otherclosed-loop controlen
dc.subject.othersoft matteren
dc.subject.otherlatencyen
dc.subject.othernonlocal controlen
dc.subject.otherspatiotemporal dynamicsen
dc.subject.otherdouble delayen
dc.titleDissipative systems with nonlocal delayed feedback controlen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber113010en
dcterms.bibliographicCitation.doi10.1088/1367-2630/aae998en
dcterms.bibliographicCitation.issue11en
dcterms.bibliographicCitation.journaltitleNew Journal of Physicsen
dcterms.bibliographicCitation.originalpublishernameIOP Publishingen
dcterms.bibliographicCitation.originalpublisherplaceLondonen
dcterms.bibliographicCitation.volume20en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Theoretische Physik::FG Statistische Physik weicher Materie und biologischer Systemede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Statistische Physik weicher Materie und biologischer Systemede
tub.affiliation.instituteInst. Theoretische Physikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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