Matches in SemOpenAlex for { <https://semopenalex.org/work/W2034694150> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W2034694150 endingPage "414" @default.
- W2034694150 startingPage "391" @default.
- W2034694150 abstract "This paper is primarily a numerical study of the fixed-point bifurcation loci — saddle-node, period-doubling and Hopf bifurcations — present in the family: [Formula: see text] where z is a complex dynamic (phase) variable, [Formula: see text] its complex conjugate, and C and A are complex parameters. We treat the parameter C as a primary parameter and A as a secondary parameter, asking how the bifurcation loci projected to the C plane change as the auxiliary parameter A is varied. For A=0, the resulting two-real-parameter family is a familiar one-complex-parameter quadratic family, and the local fixed-point bifurcation locus is the main cardioid of the Mandlebrot set. For A ≠ 0, the resulting two-real-parameter families are not complex analytic, but are still analytic (quadratic) when viewed as a map of ℛ 2 . Saddle-node and period-doubling loci evolve from points on the main cardioid for A=0 into closed curves for A ≠ 0. As A is varied further from 0 in the complex plane, the three sets interact in a variety of interesting ways. More generally, we discuss bifurcations of families of maps with some parameters designated as primary and the rest as auxiliary. The auxiliary parameter space is then divided into equivalence classes with respect to a specified set of bifurcation loci. This equivalence is defined by the existence of a diffeomorphism of corresponding primary parameter spaces which preserves the specified set of specified bifurcation loci. In our study there is a huge amount of complexity added by specifying the three fixed-point bifurcation loci together, rather than one at a time. We also provide a preliminary classification of the types of codimension-one bifurcations one should expect in general studies of families of two-parameter families of maps of the plane. Comments on numerical continuation techniques are provided as well." @default.
- W2034694150 created "2016-06-24" @default.
- W2034694150 creator A5065898862 @default.
- W2034694150 creator A5071572985 @default.
- W2034694150 date "2000-02-01" @default.
- W2034694150 modified "2023-09-27" @default.
- W2034694150 title "REAL CONTINUATION FROM THE COMPLEX QUADRATIC FAMILY: FIXED-POINT BIFURCATION SETS" @default.
- W2034694150 cites W2037497024 @default.
- W2034694150 cites W2058251174 @default.
- W2034694150 cites W2087087060 @default.
- W2034694150 doi "https://doi.org/10.1142/s0218127400000256" @default.
- W2034694150 hasPublicationYear "2000" @default.
- W2034694150 type Work @default.
- W2034694150 sameAs 2034694150 @default.
- W2034694150 citedByCount "16" @default.
- W2034694150 countsByYear W20346941502013 @default.
- W2034694150 countsByYear W20346941502014 @default.
- W2034694150 countsByYear W20346941502015 @default.
- W2034694150 crossrefType "journal-article" @default.
- W2034694150 hasAuthorship W2034694150A5065898862 @default.
- W2034694150 hasAuthorship W2034694150A5071572985 @default.
- W2034694150 hasBestOaLocation W20346941502 @default.
- W2034694150 hasConcept C101225446 @default.
- W2034694150 hasConcept C104317684 @default.
- W2034694150 hasConcept C121332964 @default.
- W2034694150 hasConcept C129844170 @default.
- W2034694150 hasConcept C134306372 @default.
- W2034694150 hasConcept C158622935 @default.
- W2034694150 hasConcept C165150564 @default.
- W2034694150 hasConcept C165263651 @default.
- W2034694150 hasConcept C185592680 @default.
- W2034694150 hasConcept C194271172 @default.
- W2034694150 hasConcept C202444582 @default.
- W2034694150 hasConcept C2524010 @default.
- W2034694150 hasConcept C2781349735 @default.
- W2034694150 hasConcept C28826006 @default.
- W2034694150 hasConcept C33923547 @default.
- W2034694150 hasConcept C55493867 @default.
- W2034694150 hasConcept C55610538 @default.
- W2034694150 hasConcept C61445026 @default.
- W2034694150 hasConcept C62520636 @default.
- W2034694150 hasConcept C73586568 @default.
- W2034694150 hasConcept C84597430 @default.
- W2034694150 hasConcept C85075877 @default.
- W2034694150 hasConceptScore W2034694150C101225446 @default.
- W2034694150 hasConceptScore W2034694150C104317684 @default.
- W2034694150 hasConceptScore W2034694150C121332964 @default.
- W2034694150 hasConceptScore W2034694150C129844170 @default.
- W2034694150 hasConceptScore W2034694150C134306372 @default.
- W2034694150 hasConceptScore W2034694150C158622935 @default.
- W2034694150 hasConceptScore W2034694150C165150564 @default.
- W2034694150 hasConceptScore W2034694150C165263651 @default.
- W2034694150 hasConceptScore W2034694150C185592680 @default.
- W2034694150 hasConceptScore W2034694150C194271172 @default.
- W2034694150 hasConceptScore W2034694150C202444582 @default.
- W2034694150 hasConceptScore W2034694150C2524010 @default.
- W2034694150 hasConceptScore W2034694150C2781349735 @default.
- W2034694150 hasConceptScore W2034694150C28826006 @default.
- W2034694150 hasConceptScore W2034694150C33923547 @default.
- W2034694150 hasConceptScore W2034694150C55493867 @default.
- W2034694150 hasConceptScore W2034694150C55610538 @default.
- W2034694150 hasConceptScore W2034694150C61445026 @default.
- W2034694150 hasConceptScore W2034694150C62520636 @default.
- W2034694150 hasConceptScore W2034694150C73586568 @default.
- W2034694150 hasConceptScore W2034694150C84597430 @default.
- W2034694150 hasConceptScore W2034694150C85075877 @default.
- W2034694150 hasIssue "02" @default.
- W2034694150 hasLocation W20346941501 @default.
- W2034694150 hasLocation W20346941502 @default.
- W2034694150 hasLocation W20346941503 @default.
- W2034694150 hasOpenAccess W2034694150 @default.
- W2034694150 hasPrimaryLocation W20346941501 @default.
- W2034694150 hasRelatedWork W1018704693 @default.
- W2034694150 hasRelatedWork W2009098071 @default.
- W2034694150 hasRelatedWork W2034694150 @default.
- W2034694150 hasRelatedWork W2072703891 @default.
- W2034694150 hasRelatedWork W2807556703 @default.
- W2034694150 hasRelatedWork W2895443674 @default.
- W2034694150 hasRelatedWork W2963509730 @default.
- W2034694150 hasRelatedWork W3123487452 @default.
- W2034694150 hasRelatedWork W4225463472 @default.
- W2034694150 hasRelatedWork W4301094765 @default.
- W2034694150 hasVolume "10" @default.
- W2034694150 isParatext "false" @default.
- W2034694150 isRetracted "false" @default.
- W2034694150 magId "2034694150" @default.
- W2034694150 workType "article" @default.