In this paper, we investigate the role of topology on
synchronization, a fundamental feature of many technological and
biological fields. We study it in Hindmarsh-Rose neural networks,
with electrical and chemical synapses, where neurons are placed on
a bi-dimensional lattice, folded on a torus, and the synapses are
set according to several topologies. In addition to the standard
topologies used in other studies, we introduce a new model that
generalizes the Barabási-Albert scale-free model, taking into
account the physical distance between nodes. Such a model, because
of its plausibility both in the static characteristics and in the
dynamical evolution, is a good representation for those real
networks (such as a network of neurons) whose edges are not
costless. We investigate synchronization in several topologies;
the results strongly depend on the adopted synapse model.
Mathematics Subject Classification: 92C29.