File Download
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.23919/ECC.2013.6669160
- Scopus: eid_2-s2.0-84893266924
Supplementary
-
Citations:
- Scopus: 0
- Appears in Collections:
Conference Paper: On the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Space
Title | On the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Space |
---|---|
Authors | |
Keywords | Nonlinear system theory Chaotic systems |
Issue Date | 2013 |
Publisher | I E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6657188 |
Citation | 12th European Control Conference (ECC 2013), Zurich, Switzerland, 17-19 July 2013. In European Control Conference, 2013, p. 670-675 How to Cite? |
Abstract | 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. |
Description | WeB6 Regular Session: Nonlinear System Theory II, Paper WeB6.3 |
Persistent Identifier | http://hdl.handle.net/10722/198883 |
ISBN |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Chesi, G | - |
dc.contributor.author | Tanaka, G | - |
dc.contributor.author | Hirata, Y | - |
dc.contributor.author | Aihara, K | - |
dc.date.accessioned | 2014-07-14T07:37:09Z | - |
dc.date.available | 2014-07-14T07:37:09Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | 12th European Control Conference (ECC 2013), Zurich, Switzerland, 17-19 July 2013. In European Control Conference, 2013, p. 670-675 | - |
dc.identifier.isbn | 9783033039629 | - |
dc.identifier.uri | http://hdl.handle.net/10722/198883 | - |
dc.description | WeB6 Regular Session: Nonlinear System Theory II, Paper WeB6.3 | - |
dc.description.abstract | 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.language | eng | - |
dc.publisher | I E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6657188 | - |
dc.relation.ispartof | European Control Conference | - |
dc.subject | Nonlinear system theory | - |
dc.subject | Chaotic systems | - |
dc.title | On the Analysis of the Bifurcation Sets of Equilibrium Points in Parameter Space | en_US |
dc.type | Conference_Paper | en_US |
dc.identifier.email | Chesi, G: chesi@eee.hku.hk | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.23919/ECC.2013.6669160 | - |
dc.identifier.scopus | eid_2-s2.0-84893266924 | - |
dc.identifier.hkuros | 230391 | - |
dc.identifier.spage | 670 | - |
dc.identifier.epage | 675 | - |
dc.publisher.place | United States | - |