Perturbation methods are used to solve the eigenvalue problem for cortical pattern formation in the presence of long-range neural connections. Such connections have a crystallinelike structure that breaks Euclidean symmetry to the discrete symmetry of a planar lattice group. Conditions for marginal stability are derived with the associated eigenmodes identified as Bloch waves.

• Received 26 February 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.088101