  The model of scientific paradigms spreading throughout the community of
agents with memory is analyzed using the master equation. The case of two
competing ideas is considered for various networks of interactions, including
agents placed at Erd\H{o}s-R\'{e}nyi graphs or complete graphs. The pace of
adopting a new idea by a community is analyzed, along with the distribution of
periods after which a new idea replaces the old one. The approach is extended
for the chain topology onto the more general case when more than two ideas
compete. Our analytical results are in agreement with numerical simulations.
