Bump competition and lattice solutions in two-dimensional neural fields

Optimal twist angle for a graphene-like bilayer

The first optimal-or 'magic'-angle leading to the nullity of the Dirac/Fermi velocity for twisted bilayer graphene is re-evaluated in the Bistritzer-MacDonald set-up (Bistritzer and MacDonald 2011Proc. Natl Acad. Sci.10812233-7). From the details of that calculation we study the resulting alterations when the properties of the two layers are not exactly the same. A moiré combination of lattices without relative rotation but with different spacing lengths may also lead to a vanishing Dirac velocity. Hopping amplitudes can vary as well, and curvature is one of the possible causes for their change. In the case of small curvature values and situations dominated by hopping energy scales, the optimal angle becomes wider than in the 'flat' case.

'Two vs one' rivalry by the Loxley-Robinson model

We apply the competitive model of Loxley and Robinson (Phys Rev Lett 102:258701, 2009. doi: 10.1103/PhysRevLett.102.258701 ) to the study of a special case of visual rivalry. Three-peaked inputs with maxima at symmetrical locations are introduced, and the role of three-bump configurations is then considered. The model yields conditions for what can be interpreted as a bistable percept analogous to the one-dimensional version of a competition between the central and flanking parts of an image.