  This paper investigates the conditions for the formation of local bumps in
the activity of binary attractor neural networks with spatially dependent
connectivity. We show that these formations are observed when asymmetry between
the activity during the retrieval and learning is imposed. Analytical
approximation for the order parameters is derived. The corresponding phase
diagram shows a relatively large and stable region, where this effect is
observed, although the critical storage and the information capacities
drastically decrease inside that region. We demonstrate that the stability of
the network, when starting from the bump formation, is larger than the
stability when starting even from the whole pattern. Finally, we show a very
good agreement between the analytical results and the simulations performed for
different topologies of the network.

Disordered Systems and Neural Networks;Soft Condensed Matter