FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2115869817> ?p ?o ?g. }

• W2115869817 endingPage "115" @default.
• W2115869817 startingPage "73" @default.
• W2115869817 abstract "In this article, we analyze the three-component reaction-diffusion system originally developed by Schenk et al. (PRL 78:3781–3784, 1997). The system consists of bistable activator-inhibitor equations with an additional inhibitor that diffuses more rapidly than the standard inhibitor (or recovery variable). It has been used by several authors as a prototype three-component system that generates rich pulse dynamics and interactions, and this richness is the main motivation for the analysis we present. We demonstrate the existence of stationary one-pulse and two-pulse solutions, and travelling one-pulse solutions, on the real line, and we determine the parameter regimes in which they exist. Also, for one-pulse solutions, we analyze various bifurcations, including the saddle-node bifurcation in which they are created, as well as the bifurcation from a stationary to a travelling pulse, which we show can be either subcritical or supercritical. For two-pulse solutions, we show that the third component is essential, since the reduced bistable two-component system does not support them. We also analyze the saddle-node bifurcation in which two-pulse solutions are created. The analytical method used to construct all of these pulse solutions is geometric singular perturbation theory, which allows us to show that these solutions lie in the transverse intersections of invariant manifolds in the phase space of the associated six-dimensional travelling wave system. Finally, as we illustrate with numerical simulations, these solutions form the backbone of the rich pulse dynamics this system exhibits, including pulse replication, pulse annihilation, breathing pulses, and pulse scattering, among others." @default.
• W2115869817 created "2016-06-24" @default.
• W2115869817 creator A5010016067 @default.
• W2115869817 creator A5017462751 @default.
• W2115869817 creator A5087776335 @default.
• W2115869817 date "2008-09-05" @default.
• W2115869817 modified "2023-09-25" @default.
• W2115869817 title "Pulse Dynamics in a Three-Component System: Existence Analysis" @default.
• W2115869817 cites W1545752770 @default.
• W2115869817 cites W1599649638 @default.
• W2115869817 cites W1978071915 @default.
• W2115869817 cites W1978486451 @default.
• W2115869817 cites W1981858478 @default.
• W2115869817 cites W1986364663 @default.
• W2115869817 cites W1986864730 @default.
• W2115869817 cites W1989095982 @default.
• W2115869817 cites W1990231806 @default.
• W2115869817 cites W1996557767 @default.
• W2115869817 cites W2003754616 @default.
• W2115869817 cites W2006865148 @default.
• W2115869817 cites W2014241231 @default.
• W2115869817 cites W2016767879 @default.
• W2115869817 cites W2041496883 @default.
• W2115869817 cites W2055705183 @default.
• W2115869817 cites W2059625173 @default.
• W2115869817 cites W2059873786 @default.
• W2115869817 cites W2061958555 @default.
• W2115869817 cites W2135690127 @default.
• W2115869817 cites W2141061348 @default.
• W2115869817 cites W2171207028 @default.
• W2115869817 cites W4236765228 @default.
• W2115869817 cites W99189181 @default.
• W2115869817 doi "https://doi.org/10.1007/s10884-008-9125-2" @default.
• W2115869817 hasPublicationYear "2008" @default.
• W2115869817 type Work @default.
• W2115869817 sameAs 2115869817 @default.
• W2115869817 citedByCount "65" @default.
• W2115869817 countsByYear W21158698172012 @default.
• W2115869817 countsByYear W21158698172013 @default.
• W2115869817 countsByYear W21158698172014 @default.
• W2115869817 countsByYear W21158698172015 @default.
• W2115869817 countsByYear W21158698172016 @default.
• W2115869817 countsByYear W21158698172017 @default.
• W2115869817 countsByYear W21158698172018 @default.
• W2115869817 countsByYear W21158698172019 @default.
• W2115869817 countsByYear W21158698172020 @default.
• W2115869817 countsByYear W21158698172021 @default.
• W2115869817 countsByYear W21158698172022 @default.
• W2115869817 countsByYear W21158698172023 @default.
• W2115869817 crossrefType "journal-article" @default.
• W2115869817 hasAuthorship W2115869817A5010016067 @default.
• W2115869817 hasAuthorship W2115869817A5017462751 @default.
• W2115869817 hasAuthorship W2115869817A5087776335 @default.
• W2115869817 hasBestOaLocation W21158698171 @default.
• W2115869817 hasConcept C120665830 @default.
• W2115869817 hasConcept C121231716 @default.
• W2115869817 hasConcept C121332964 @default.
• W2115869817 hasConcept C134306372 @default.
• W2115869817 hasConcept C158622935 @default.
• W2115869817 hasConcept C2780167933 @default.
• W2115869817 hasConcept C2781349735 @default.
• W2115869817 hasConcept C33923547 @default.
• W2115869817 hasConcept C51544822 @default.
• W2115869817 hasConcept C62520636 @default.
• W2115869817 hasConcept C78045399 @default.
• W2115869817 hasConcept C94915269 @default.
• W2115869817 hasConcept C97292510 @default.
• W2115869817 hasConceptScore W2115869817C120665830 @default.
• W2115869817 hasConceptScore W2115869817C121231716 @default.
• W2115869817 hasConceptScore W2115869817C121332964 @default.
• W2115869817 hasConceptScore W2115869817C134306372 @default.
• W2115869817 hasConceptScore W2115869817C158622935 @default.
• W2115869817 hasConceptScore W2115869817C2780167933 @default.
• W2115869817 hasConceptScore W2115869817C2781349735 @default.
• W2115869817 hasConceptScore W2115869817C33923547 @default.
• W2115869817 hasConceptScore W2115869817C51544822 @default.
• W2115869817 hasConceptScore W2115869817C62520636 @default.
• W2115869817 hasConceptScore W2115869817C78045399 @default.
• W2115869817 hasConceptScore W2115869817C94915269 @default.
• W2115869817 hasConceptScore W2115869817C97292510 @default.
• W2115869817 hasIssue "1" @default.
• W2115869817 hasLocation W21158698171 @default.
• W2115869817 hasLocation W21158698172 @default.
• W2115869817 hasLocation W21158698173 @default.
• W2115869817 hasLocation W21158698174 @default.
• W2115869817 hasOpenAccess W2115869817 @default.
• W2115869817 hasPrimaryLocation W21158698171 @default.
• W2115869817 hasRelatedWork W1973994723 @default.
• W2115869817 hasRelatedWork W2031256957 @default.
• W2115869817 hasRelatedWork W2068647081 @default.
• W2115869817 hasRelatedWork W2090154871 @default.
• W2115869817 hasRelatedWork W2788310402 @default.
• W2115869817 hasRelatedWork W2969349722 @default.
• W2115869817 hasRelatedWork W3119129405 @default.
• W2115869817 hasRelatedWork W3152680424 @default.
• W2115869817 hasRelatedWork W4295886850 @default.
• W2115869817 hasRelatedWork W78288096 @default.
• W2115869817 hasVolume "21" @default.

• next