Boltzmann-like and Boltzmann-Fokker-Planck Equations as a Foundation of Behavioral Models

Abstract

It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair interactions. As most important social pair interactions imitative and avoidance processes are distinguished. The resulting model turns out to include as special cases many theoretical concepts of the social sciences. A Kramers-Moyal expansion of the Boltzmann-like equations leads to the Boltzmann-Fokker-Planck equations, which allows the introduction of ``social forces'' and ``social fields''. A social field reflects the influence of the public opinion, social norms and trends on behaviorial changes. It is not only given by external factors (the environment) but also by the interactions of the individuals. Variations of the individual behavior are taken into account by diffusion coefficients.

For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html

References in corpus (4)

• A Fluid Dynamic Model for the Movement of Pedestrians
• Interrelations between Stochastic Equations for Systems with Pair Interactions
• Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory
• A Mathematical Model for Behavioral Changes by Pair Interactions and Its Relation to Game Theory

Cited by in corpus (18)

• Social Force Model for Pedestrian Dynamics
• Statistical physics of social dynamics
• Traffic and Related Self-Driven Many-Particle Systems
• Recent advances in opinion propagation dynamics: A 2020 Survey
• Optimal Self-Organization
• From classical to modern opinion dynamics
• Deep reinforcement learning with a particle dynamics environment applied to emergency evacuation of a room with obstacles
• Early exclusion leads to cyclical cooperation in repeated group interactions
• From Microscopic to Macroscopic Traffic Models
• Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power
• Drift reversal in asymmetric coevolutionary conflicts: Influence of microscopic processes and population size
• Self-Organization in Space and Induced by Fluctuations
• An energy-based interaction model for population opinion dynamics with topic coupling
• The Paradox of Information Access: On Modeling Social-Media-Induced Polarization
• A Contracted Path Integral Solution of the Discrete Master Equation
• Hate: no choice. Agent simulations
• Structured populations facilitate cooperation in policed Public Goods Games
• Combination of institutional incentives for cooperative governance of risky commons