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Self-organized collapse of societies.

Alexander Jochim1, Stefan Bornholdt1

  • 1University of Bremen, Institute for Theoretical Physics, Germany.

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|January 21, 2026
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Summary

Human societies face instability due to economic inequality and social factors. A minimal mathematical model reveals that broad wealth distributions drive social unrest and economic boom-and-bust cycles.

Area of Science:

  • Sociology
  • Economics
  • Mathematical Modeling
  • Complexity Science

Background:

  • Recurring patterns in historical data suggest economic inequality and social factors drive societal instability.
  • Existing models of societal instability are primarily macroscopic.
  • Minimal mathematical models may reveal underlying mechanisms of societal dynamics.

Purpose of the Study:

  • To develop a minimal mathematical model integrating economic growth and social dissatisfaction.
  • To investigate the relationship between wealth distribution and societal instability.
  • To explore the emergence of boom-and-bust cycles in social systems.

Main Methods:

  • Combined a simple economic growth mechanism with a social dissatisfaction spreading mechanism.

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  • Utilized mathematical modeling to simulate societal dynamics.
  • Analyzed the impact of broad wealth distributions (power law) on social phenomena.

    • Main Results:

    • Broad wealth distributions, generated by the economic mechanism, trigger social unrest and wealth destruction.
    • The model demonstrates an emerging pattern of boom and bust cycles.
    • Model timescales show good agreement with empirical data.
    • Emphasized the role of broad (power law) wealth distributions in dynamical social phenomena.

    Conclusions:

    • Minimal mathematical models can capture essential dynamics of societal instability.
    • Economic inequality, particularly broad wealth distributions, is a critical factor in social unrest and economic cycles.
    • The study highlights the predictive power of understanding wealth distribution for social phenomena.