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dc.contributor.authorDercole, Fabio
dc.contributor.authorDella Rossa, Fabio
dc.contributor.authorColombo, Alessandro
dc.contributor.authorKuznetsov, Yuri A.
dc.date.accessioned2012-09-05T12:53:18Z
dc.date.available2012-09-05T12:53:18Z
dc.date.issued2011-12
dc.date.submitted2011-10
dc.identifier.issn1536-0040
dc.identifier.urihttp://hdl.handle.net/1721.1/72513
dc.description.abstractWe contribute to the analysis of codimension-two bifurcations in discontinuous systems by studying all equilibrium bifurcations of 2D Filippov systems that involve a sliding limit cycle. There are only two such local bifurcations: (1) a degenerate boundary focus, which we call the homoclinic boundary focus (HBF), and (2) the boundary Hopf (BH). We prove that—besides local bifurcations of equilibria and pseudoequilibria—the universal unfolding of the HBF singularity includes a codimension-one global bifurcation at which a sliding homoclinic orbit to a pseudosaddle exists, while that of the BH singularity has a codimension-one bifurcation curve along which a cycle grazing occurs. We define two canonical forms, one for each singularity, to which a generic 2D Filippov system can be locally reduced by smooth changes of variables and parameters and time reparametrization. Explicit genericity conditions are also provided, as well as the asymptotics of the bifurcation curves in the two-parameter space. We show that both studied codimension-two bifurcations occur in a known 2D Filippov system modeling an ecosystem subject to on-off harvesting control, and we provide two Mathematica scripts that automatize all computations.en_US
dc.language.isoen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/100812549en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSIAMen_US
dc.titleTwo Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systemsen_US
dc.typeArticleen_US
dc.identifier.citationDercole, Fabio et al. “Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems.” SIAM Journal on Applied Dynamical Systems 10.4 (2011): 1525–1553. © 2011 Society for Industrial and Applied Mathematics.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.approverColombo, Alessandro
dc.contributor.mitauthorColombo, Alessandro
dc.relation.journalSIAM Journal on Applied Dynamical Systemsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsDercole, Fabio; Della Rossa, Fabio; Colombo, Alessandro; Kuznetsov, Yuri A.en
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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