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Updated: Nov 4, 2025

The HoneyComb Paradigm for Research on Collective Human Behavior

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Network Structured Kinetic Models of Social Interactions.

Martin Burger¹

¹Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstr. 11, D 91058 Erlangen, Germany.

Vietnam Journal of Mathematics

|May 24, 2021

Summary

This study develops models for social interactions, considering network structures and asymmetric agent roles. The models explain phenomena like language evolution and epidemic spread using reaction-diffusion equations.

Keywords:

Kinetic models Network structured interactions Nonlinear nonlocal equations Reaction-diffusion equations Social networks

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Last Updated: Nov 4, 2025

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Published on: February 25, 2011

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats

Published on: January 18, 2013

Area of Science:

Mathematical Modeling
Social Dynamics
Statistical Mechanics

Background:

Classical statistical mechanics often assumes symmetric roles in interactions.
Social processes exhibit complex network structures and asymmetric agent roles.
Understanding these dynamics requires advanced modeling techniques.

Purpose of the Study:

To derive meso- and macroscopic models for social interactions.
To incorporate network structures and asymmetric agent roles into these models.
To explain emergent spatial phenomena in social systems.

Main Methods:

Development of kinetic equations for mesoscopic description.
Derivation of macroscopic models from monokinetic solutions.
Application of nonlocal reaction-diffusion equations.

Main Results:

Obtained kinetic equations describing asymmetric interactions.
Derived nonlocal reaction-diffusion equations from kinetic models.
Demonstrated ability to explain spatial phase separation.

Conclusions:

The derived models effectively capture social interaction dynamics.
Reaction-diffusion equations can explain emergent spatial patterns.
The approach is applicable to diverse social phenomena like language, norms, and epidemics.