Although a number of models have been developed to investigate the emergence
of culture and evolutionary phases in social systems, one important aspect has
not yet been sufficiently emphasized. This is the structure of the underlaying
network of social relations serving as channels in transmitting cultural
traits, which is expected to play a crucial role in the evolutionary processes
in social systems. In this paper we contribute to the understanding of the role
of the network structure by developing a layered ego-centric network structure
based model, inspired by the social brain hypothesis, to study transmission of
cultural traits and their evolution in social network. For this model we first
find analytical results in the spirit of mean-field approximation and then to
validate the results we compare them with the results of extensive numerical
simulations.Comment: 10 pages, 2 figure
