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2020-03-23Zeitschriftenartikel DOI: 10.1088/1367-2630/ab7a05
Monte Carlo basin bifurcation analysis
dc.contributor.authorGelbrecht, Maximilian
dc.contributor.authorKurths, Jürgen
dc.contributor.authorHellmann, Frank
dc.date.accessioned2022-03-25T12:30:01Z
dc.date.available2022-03-25T12:30:01Z
dc.date.issued2020-03-23none
dc.date.updated2022-02-11T18:14:52Z
dc.identifier.urihttp://edoc.hu-berlin.de/18452/25038
dc.description.abstractMany high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds–Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart–Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language.eng
dc.description.sponsorshipBundesministerium für Bildung und Forschung https://doi.org/10.13039/501100002347
dc.description.sponsorshipDeutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659
dc.description.sponsorshipFAPESP (Fundaçāo de Amparo à Pesquisa do Estado de São Paulo
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY 4.0) Attribution 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectnonlinear dynamicseng
dc.subjectcomplex systemseng
dc.subjectbifurcationeng
dc.subjectbasin stabilityeng
dc.subject.ddc530 Physiknone
dc.titleMonte Carlo basin bifurcation analysisnone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/25038-2
dc.identifier.doi10.1088/1367-2630/ab7a05none
dc.identifier.doihttp://dx.doi.org/10.18452/24384
dc.type.versionpublishedVersionnone
local.edoc.container-titleNew journal of physics : the open-access journal for physicsnone
local.edoc.pages17none
local.edoc.type-nameZeitschriftenartikel
local.edoc.institutionMathematisch-Naturwissenschaftliche Fakultätnone
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
local.edoc.container-publisher-nameIOPnone
local.edoc.container-publisher-place[London]none
local.edoc.container-volume22none
local.edoc.container-issue3none
dc.description.versionPeer Reviewednone
local.edoc.container-articlenumber033032none
dc.identifier.eissn1367-2630

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