Tipping phenomena and points of no return in ecosystems: beyond classical bifurcations

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dc.contributor.authorO'Keefe, Paul E.
dc.contributor.authorWieczorek, Sebastian
dc.contributor.funderHorizon 2020en
dc.date.accessioned2020-11-27T13:29:38Z
dc.date.available2020-11-27T13:29:38Z
dc.date.issued2020-10-22
dc.date.updated2020-11-27T13:14:53Z
dc.description.abstractWe discuss tipping phenomena in nonautonomous systems using an example of a bistable ecosystem model with environmental changes represented by time-varying parameters [Scheffer et al., Ecosystems, 11 (2008), pp. 275--279]. We give simple testable criteria for the occurrence of nonautonomous tipping from the herbivore-dominating equilibrium to the plant-only equilibrium using global properties of the autonomous frozen system with fixed-in-time parameters. To begin with, we use classical autonomous bifurcation analysis to identify a codimension-three degenerate Bogdanov--Takens bifurcation: the source of a dangerous subcritical Hopf bifurcation and the organizing center for bifurcation-induced tipping (B-tipping). Then, we introduce the concept of basin instability for equilibria to identify parameter paths along which genuine nonautonomous rate-induced tipping (R-tipping) occurs without crossing any classical autonomous bifurcations. We explain nonautonomous R-tipping in terms of maximal canard trajectories and produce nonautonomous tipping diagrams in the plane of the magnitude and rate of a parameter shift to uncover intriguing R-tipping tongues and wiggling tipping-tracking bifurcation curves. Discussion of nontrivial dynamics arising from the interaction between B-tipping and R-tipping identifies “points of no return” where tipping cannot be prevented by the parameter trend reversal and “points of return tipping” where tipping is inadvertently induced by the parameter trend reversal. Our results give new insight into the sensitivity of ecosystems to the magnitudes and rates of environmental change. Finally, a comparison between “tilted” saddle-node and subcritical Hopf normal forms reveals some universal tipping properties due to basin instability, a generic dangerous bifurcation, or the combination of both.en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationO'Keeffe, P. E. and Wieczorek, S. (2020) 'Tipping Phenomena and Points of No Return in Ecosystems: Beyond Classical Bifurcations', SIAM Journal on Applied Dynamical Systems, 19(4), pp. 2371-2402. doi: 10.1137/19M1242884en
dc.identifier.doi10.1137/19M1242884en
dc.identifier.endpage2402en
dc.identifier.issn1536-0040
dc.identifier.issued4en
dc.identifier.journaltitleSIAM Journal on Applied Dynamical Systemsen
dc.identifier.startpage2371en
dc.identifier.urihttps://hdl.handle.net/10468/10788
dc.identifier.volume19en
dc.language.isoenen
dc.publisherSociety for Industrial and Applied Mathematic, SIAMen
dc.relation.projectinfo:eu-repo/grantAgreement/EC/H2020::MSCA-ITN-ETN/643073/EU/Critical Transitions in Complex Systems/CRITICSen
dc.relation.urihttps://epubs.siam.org/doi/pdf/10.1137/19M1242884
dc.rights© 2020, Society for Industrial and Applied Mathematicsen
dc.subjectTipping pointsen
dc.subjectR-tippingen
dc.subjectCritical ratesen
dc.subjectNonautonomous bifurcationsen
dc.subjectB-tippingen
dc.subjectTipping diagramsen
dc.subjectEcosystem dynamicsen
dc.subjectBogdanov--Takens bifurcationen
dc.subjectBasin instabilityen
dc.subjectMaximal canardsen
dc.subjectSlow passage through subcritical Hopf bifurcationen
dc.subjectPoints of returnen
dc.subjectPoints of no returnen
dc.subjectPoints of return tippingen
dc.titleTipping phenomena and points of no return in ecosystems: beyond classical bifurcationsen
dc.typeArticle (peer-reviewed)en
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