The model [1] of scientific paradigms spreading throughout the community of agents with memory is analyzed using the master equation. Our analytical solutions are compared with numerical simulations. The case of two competing ideas is considered for various networks of interactions, including agents placed at chains, complete graphs, ER graphs, stars, square lattices and BA graphs. The pace of adopting a new idea by the community is analyzed, along with the distribution of periods between dominating paradigm shifts. We study the impact of the interactions topology onto the dynamics, as well as the role of hubs in the process. The approach is extended for the chain topology onto the more general case when more than two ideas compete.
The preprint of our paper can be found at [2].

[1] S. Bornholdt, M. H. Jensen, and K. Sneppen, Phys. Rev. Lett., 106(5):058701, Feb 2011.
[2] P. Kondratiuk, G. Siudem, and J. A. Holyst, arXiv:1106.0438v2 [physics.soc-ph], June 2011.

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