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Conference Paper: On the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Space

TitleOn the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Space
Authors
KeywordsNonlinear system theory
Chaotic systems
Issue Date2013
PublisherI E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6657188
Citation
European Control Conference (ECC), Zurich, Switzerland, 17-19 July 2013. In European Control Conference, 2013, p. 670-675 How to Cite?
AbstractAbstract: This paper addresses the problems of characterizing and estimating the bifurcation sets of equilibrium points in multi-parameter space of a class of nonlinear dynamical systems. Specifically, we investigate the sets of parameters that lead to saddle-node bifurcations and Hopf bifurcations at an equilibrium point of interest. First, a characterization of these sets is provided in terms of the zeros of some functions. Second, this characterization is exploited to estimate such sets through convex programming for the case of polynomial dynamical systems. In particular, two conditions are proposed for establishing whether a sublevel set of a given polynomial does not contain parameters that lead to bifurcations. By using these conditions, the largest of such sublevel sets can be estimated by solving an eigenvalue problem. Some numerical examples illustrate the proposed results.
DescriptionWeB6 Regular Session: Nonlinear System Theory II, Paper WeB6.3
Persistent Identifierhttp://hdl.handle.net/10722/198883
ISBN

 

DC FieldValueLanguage
dc.contributor.authorChesi, G-
dc.contributor.authorTanaka, G-
dc.contributor.authorHirata, Y-
dc.contributor.authorAihara, K-
dc.date.accessioned2014-07-14T07:37:09Z-
dc.date.available2014-07-14T07:37:09Z-
dc.date.issued2013-
dc.identifier.citationEuropean Control Conference (ECC), Zurich, Switzerland, 17-19 July 2013. In European Control Conference, 2013, p. 670-675-
dc.identifier.isbn9783033039629-
dc.identifier.urihttp://hdl.handle.net/10722/198883-
dc.descriptionWeB6 Regular Session: Nonlinear System Theory II, Paper WeB6.3-
dc.description.abstractAbstract: This paper addresses the problems of characterizing and estimating the bifurcation sets of equilibrium points in multi-parameter space of a class of nonlinear dynamical systems. Specifically, we investigate the sets of parameters that lead to saddle-node bifurcations and Hopf bifurcations at an equilibrium point of interest. First, a characterization of these sets is provided in terms of the zeros of some functions. Second, this characterization is exploited to estimate such sets through convex programming for the case of polynomial dynamical systems. In particular, two conditions are proposed for establishing whether a sublevel set of a given polynomial does not contain parameters that lead to bifurcations. By using these conditions, the largest of such sublevel sets can be estimated by solving an eigenvalue problem. Some numerical examples illustrate the proposed results.-
dc.languageeng-
dc.publisherI E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6657188-
dc.relation.ispartofEuropean Control Conference-
dc.rightsEuropean Control Conference. Copyright © I E E E.-
dc.rights©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectNonlinear system theory-
dc.subjectChaotic systems-
dc.titleOn the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Spaceen_US
dc.typeConference_Paperen_US
dc.identifier.emailChesi, G: chesi@eee.hku.hk-
dc.description.naturepublished_or_final_version-
dc.identifier.scopuseid_2-s2.0-84893266924-
dc.identifier.hkuros230391-
dc.identifier.spage670-
dc.identifier.epage675-
dc.publisher.placeUnited States-

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