Bifurcation diagram of a cubic three-parameter autonomous system

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dc.contributor.authorBarakova, Lenka
dc.contributor.authorVolokitin, Evgenii P.
dc.date.accessioned2021-05-28T20:36:33Z
dc.date.available2021-05-28T20:36:33Z
dc.date.issued2005-07-19
dc.description.abstractIn this paper, we study the cubic three-parameter autonomous planar system ẋ1 = k1 + k2x1 - x31 - x2, ẋ2 = k3x1 - x2 where k2, k3 > 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation). We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
dc.description.departmentMathematics
dc.formatText
dc.format.extent16 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBaráková, L., & Volokitin, E. P. (2005). Bifurcation diagram of a cubic three-parameter autonomous system. <i>Electronic Journal of Differential Equations, 2005</i>(83), pp. 1-16.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13684
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectPhase portrait
dc.subjectBifurcation
dc.subjectCentral manifold
dc.subjectTopological equivalence
dc.subjectStructural stability
dc.subjectBifurcation diagram
dc.subjectLimit cycle
dc.titleBifurcation diagram of a cubic three-parameter autonomous system
dc.typeArticle

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