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Titolo:
Scalar and pseudoscalar bifurcations motivated by pattern formation on thevisual cortex
Autore:
Bressloff, PC; Cowan, JD; Golubitsky, M; Thomas, PJ;
Indirizzi:
Univ Utah, Dept Math, Salt Lake City, UT 84112 USA Univ Utah Salt Lake City UT USA 84112 Math, Salt Lake City, UT 84112 USA Univ Chicago, Dept Math, Chicago, IL 60637 USA Univ Chicago Chicago IL USA 60637 icago, Dept Math, Chicago, IL 60637 USA Univ Houston, Dept Math, Houston, TX 77204 USA Univ Houston Houston TX USA 77204 uston, Dept Math, Houston, TX 77204 USA Salk Inst Biol Studies, Computat Neurobiol Lab, San Diego, CA 92186 USA Salk Inst Biol Studies San Diego CA USA 92186 ab, San Diego, CA 92186 USA
Titolo Testata:
NONLINEARITY
fascicolo: 4, volume: 14, anno: 2001,
pagine: 739 - 775
SICI:
0951-7715(200107)14:4<739:SAPBMB>2.0.ZU;2-K
Fonte:
ISI
Lingua:
ENG
Soggetto:
MONKEY STRIATE CORTEX; SELECTION; SYMMETRY;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
15
Recensione:
Indirizzi per estratti:
Indirizzo: Bressloff, PC Univ Utah, Dept Math, Salt Lake City, UT 84112 USA Univ Utah Salt Lake City UT USA 84112 ke City, UT 84112 USA
Citazione:
P.C. Bressloff et al., "Scalar and pseudoscalar bifurcations motivated by pattern formation on thevisual cortex", NONLINEARIT, 14(4), 2001, pp. 739-775

Abstract

Bosch Vivancos, Chossat and Melbourne showed that two types of steady-state bifurcations are possible from trivial states when Euclidean equivariant systems are restricted to a planar lattice-scalar and pseudoscalar-and began the study of pseudoscalar bifurcations. The scalar bifurcations have beenwell studied since they appear in planar reaction-diffusion systems and inplane layer convection problems. Bressloff, Cowan, Golubitsky, Thomas and Wiener showed that bifurcations in models of the visual cortex naturally contain both scalar and pseudoscalar bifurcations, due to a different action of the Euclidean group in that application. In this paper, we review the symmetry discussion in Bressloff et al and wecontinue the study of pseudoscalar bifurcations. Our analysis furthers thestudy of pseudoscalar bifurcations in three ways. (a) We complete the classification of axial subgroups on the hexagonal lattice in the shortest wavevector case proving the existence of one new planform-a solution with triangular D-3 symmetry. (b) We derive bifurcation diagrams for generic bifurcations giving, in particular, the stability of solutions to perturbations in the hexagonal lattice. For the simplest (codimension zero) bifurcations, these bifurcation diagrams are identical to those derived by Golubitsky, Swift and Knobloch in the case of Benard convection when there is a midplane reflection-though thedetails in the analysis are more complicated. (c) We discuss the types of secondary states that can appear in codimension-one bifurcations tone parameter in addition to the bifurcation parameter), which include time periodic states from roll and hexagon solutions and drifting solutions from triangles (though the drifting solutions are always unstable near codimension-one bifurcations). The essential difference between scalar and pseudoscalar bifurcations appears in this discussion.

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Documento generato il 27/01/20 alle ore 07:29:06