FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4226150667> ?p ?o ?g. }

• W4226150667 endingPage "393" @default.
• W4226150667 startingPage "393" @default.
• W4226150667 abstract "<p style='text-indent:20px;'>A heterodimensional cycle consists of two saddle periodic orbits with unstable manifolds of different dimensions and a pair of connecting orbits between them. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting has shown that heterodimensional cycles may occur robustly in diffeomorphisms of dimension at least three. We consider the first explicit example of a heterodimensional cycle in the continuous-time setting, which has been identified by Zhang, Krauskopf and Kirk [<i>Discr. Contin. Dynam. Syst. A</i> <b>32</b>(8) 2825-2851 (2012)] in a four-dimensional vector-field model of intracellular calcium dynamics.</p><p style='text-indent:20px;'>We show here how a boundary-value problem set-up can be employed to determine the organization of the dynamics in a neighborhood in phase space of this heterodimensional cycle, which consists of a single connecting orbit of codimension one and an entire cylinder of structurally stable connecting orbits between two saddle periodic orbits. More specifically, we compute the relevant stable and unstable manifolds, which we visualize in different projections of phase space and as intersection sets with a suitable three-dimensional Poincaré section. In this way, we show that, locally near the intersection set of the heterodimensional cycle, the manifolds interact as described by the theory for three-dimensional diffeomorphisms. On the other hand, their global structure is more intricate, which is due to the fact that it is not possible to find a Poincaré section that is transverse to the flow everywhere. More generally, our results show that advanced numerical continuation techniques enable one to investigate how abstract concepts †such as that of a heterodimensional cycle of a diffeomorphism †arise and manifest themselves in explicit continuous-time systems from applications.</p>" @default.
• W4226150667 created "2022-05-05" @default.
• W4226150667 creator A5051081970 @default.
• W4226150667 creator A5072817844 @default.
• W4226150667 creator A5077661685 @default.
• W4226150667 creator A5078314587 @default.
• W4226150667 date "2022-01-01" @default.
• W4226150667 modified "2023-10-18" @default.
• W4226150667 title "Determining the global manifold structure of a continuous-time heterodimensional cycle" @default.
• W4226150667 cites W1259560820 @default.
• W4226150667 cites W149727665 @default.
• W4226150667 cites W152075171 @default.
• W4226150667 cites W1596321532 @default.
• W4226150667 cites W170447982 @default.
• W4226150667 cites W1966278929 @default.
• W4226150667 cites W1967721363 @default.
• W4226150667 cites W1971808848 @default.
• W4226150667 cites W1983996787 @default.
• W4226150667 cites W1984354620 @default.
• W4226150667 cites W2003884541 @default.
• W4226150667 cites W2025327182 @default.
• W4226150667 cites W2030813267 @default.
• W4226150667 cites W2034919761 @default.
• W4226150667 cites W2040995216 @default.
• W4226150667 cites W2046238971 @default.
• W4226150667 cites W2049119403 @default.
• W4226150667 cites W2050404322 @default.
• W4226150667 cites W2068136282 @default.
• W4226150667 cites W2077011938 @default.
• W4226150667 cites W2077847058 @default.
• W4226150667 cites W2077933648 @default.
• W4226150667 cites W2084882300 @default.
• W4226150667 cites W2088432334 @default.
• W4226150667 cites W2089876099 @default.
• W4226150667 cites W2091534537 @default.
• W4226150667 cites W2108836892 @default.
• W4226150667 cites W2111660337 @default.
• W4226150667 cites W2119779417 @default.
• W4226150667 cites W2121167960 @default.
• W4226150667 cites W2143054589 @default.
• W4226150667 cites W2155576832 @default.
• W4226150667 cites W2163678030 @default.
• W4226150667 cites W2168393226 @default.
• W4226150667 cites W2205816517 @default.
• W4226150667 cites W2319862208 @default.
• W4226150667 cites W2331123169 @default.
• W4226150667 cites W2592848684 @default.
• W4226150667 cites W2796312905 @default.
• W4226150667 cites W2888434284 @default.
• W4226150667 cites W2950197822 @default.
• W4226150667 cites W2963117407 @default.
• W4226150667 cites W3047305386 @default.
• W4226150667 cites W3100024187 @default.
• W4226150667 cites W3101099863 @default.
• W4226150667 cites W3105320353 @default.
• W4226150667 cites W3105365955 @default.
• W4226150667 cites W3121665402 @default.
• W4226150667 cites W3137137946 @default.
• W4226150667 cites W316919195 @default.
• W4226150667 cites W4210605524 @default.
• W4226150667 cites W4212928962 @default.
• W4226150667 cites W4302573344 @default.
• W4226150667 doi "https://doi.org/10.3934/jcd.2022008" @default.
• W4226150667 hasPublicationYear "2022" @default.
• W4226150667 type Work @default.
• W4226150667 citedByCount "3" @default.
• W4226150667 countsByYear W42261506672023 @default.
• W4226150667 crossrefType "journal-article" @default.
• W4226150667 hasAuthorship W4226150667A5051081970 @default.
• W4226150667 hasAuthorship W4226150667A5072817844 @default.
• W4226150667 hasAuthorship W4226150667A5077661685 @default.
• W4226150667 hasAuthorship W4226150667A5078314587 @default.
• W4226150667 hasBestOaLocation W42261506671 @default.
• W4226150667 hasConcept C121332964 @default.
• W4226150667 hasConcept C127413603 @default.
• W4226150667 hasConcept C134306372 @default.
• W4226150667 hasConcept C151342819 @default.
• W4226150667 hasConcept C164380108 @default.
• W4226150667 hasConcept C202444582 @default.
• W4226150667 hasConcept C33923547 @default.
• W4226150667 hasConcept C529865628 @default.
• W4226150667 hasConcept C62520636 @default.
• W4226150667 hasConcept C78519656 @default.
• W4226150667 hasConceptScore W4226150667C121332964 @default.
• W4226150667 hasConceptScore W4226150667C127413603 @default.
• W4226150667 hasConceptScore W4226150667C134306372 @default.
• W4226150667 hasConceptScore W4226150667C151342819 @default.
• W4226150667 hasConceptScore W4226150667C164380108 @default.
• W4226150667 hasConceptScore W4226150667C202444582 @default.
• W4226150667 hasConceptScore W4226150667C33923547 @default.
• W4226150667 hasConceptScore W4226150667C529865628 @default.
• W4226150667 hasConceptScore W4226150667C62520636 @default.
• W4226150667 hasConceptScore W4226150667C78519656 @default.
• W4226150667 hasIssue "3" @default.
• W4226150667 hasLocation W42261506671 @default.
• W4226150667 hasOpenAccess W4226150667 @default.
• W4226150667 hasPrimaryLocation W42261506671 @default.
• W4226150667 hasRelatedWork W1979480386 @default.

• next