Pinwheel stabilization by ocular dominance segregation

We present an analytical approach for studying the coupled development of ocular dominance and orientation preference columns. Using this approach we demonstrate that ocular dominance segregation can induce the stabilization and even the production of pinwheels by their crystallization in two types of periodic lattices. Pinwheel crystallization depends on the overall dominance of one eye over the other, a condition that is fulfilled during early cortical development. Increasing the strength of inter-map coupling induces a transition from pinwheel-free stripe solutions to intermediate and high pinwheel density states.Comment: 10 pages, 4 figure

Stochastic stability at the boundary of expanding maps

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula