Cultural propagation on social networks

Area of Science:

• Sociophysics
• Network Science
• Computational Social Science

Background:

• Cultural propagation models are essential for understanding social dynamics.
• Axelrod's model provides a foundational framework but has limitations in capturing certain social phenomena.
• Network topology and interaction dynamics significantly influence cultural spread.

Purpose of the Study:

• To present an extended model for cultural propagation on diverse network topologies.
• To incorporate majority rule dynamics into cultural change processes.
• To define a Lyapunov functional for analyzing the stability and behavior of the proposed model.

Main Methods:

• Developing a computational model for cultural trait propagation.
• Simulating the model on networks with varying topologies (e.g., random, scale-free, small-world).
• Implementing a majority-based rule for cultural trait adoption and change.
• Deriving and analyzing a Lyapunov functional to characterize system convergence.

Main Results:

• The extended model demonstrates distinct cultural propagation patterns based on network topology.
• Majority rule dynamics lead to faster consensus formation compared to previous models.
• The Lyapunov functional confirms the system's tendency towards stable cultural states.

Conclusions:

• The proposed majority-rule cultural propagation model offers a more realistic representation of social influence.
• Network structure and local majority dynamics are critical determinants of cultural evolution.
• The defined Lyapunov functional provides a powerful tool for theoretical analysis of cultural dynamics.