Analytical approach to model of scientific revolutions

TL;DR

This paper develops an analytical model using master equations to study how scientific ideas spread and replace each other within communities, considering different network structures and multiple competing ideas.

Contribution

It introduces an analytical framework for modeling the dynamics of scientific revolutions with multiple ideas and various network topologies, validated by numerical simulations.

Findings

The model accurately predicts the pace of idea adoption.

Distribution of idea replacement periods matches simulations.

Network structure influences the spread and replacement dynamics.

Abstract

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.