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The Demographic-Wealth model for cliodynamics.

Lukas Wittmann1, Christian Kuehn1

  • 1Department of Mathematics, School of Computation Information and Technology, Technical University of Munich, Garching, Germany.

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This study introduces a new Demographic-Wealth Model (DWM) as an alternative to Turchin's Demographic-Fiscal Model (DFM) for cliodynamics. The DWM uses nonlinear dynamics to explain historical secular cycles by linking population and state dynamics.

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Area of Science:

  • Cliodynamics
  • Mathematical modeling of historical processes
  • Nonlinear dynamics

Background:

  • The Demographic-Fiscal Model (DFM) by Turchin is a foundational model linking population and state dynamics.
  • Further model development and comparison are essential for advancing cliodynamics.
  • Existing models offer limited perspectives on the interplay between population and state dynamics.

Purpose of the Study:

  • To propose and analyze an alternative mathematical model to the classical Turchin Demographic-Fiscal Model (DFM).
  • To investigate the link between population and state dynamics using different modeling assumptions, particularly regarding taxation.
  • To explore the application of nonlinear dynamics tools for analyzing cliodynamic models.

Main Methods:

  • Development of a novel Demographic-Wealth Model (DWM).
  • Application of nonlinear dynamics tools, including existence theory for periodic orbits.
  • Analytical and numerical bifurcation analysis, with a focus on Hopf bifurcations and equilibria.

Main Results:

  • The Demographic-Wealth Model (DWM) exhibits complex dynamics, including various Hopf bifurcations.
  • Analysis reveals the significant role of Hopf bifurcations in population and state dynamics.
  • Exceeding critical parameter values leads to periodic behavior and limit cycles, analogous to the ecological "paradox of enrichment".

Conclusions:

  • The Demographic-Wealth Model (DWM) offers a simplified framework for understanding secular cycles observed in historical data.
  • Nonlinear dynamics tools, especially bifurcation analysis, are valuable for cliodynamic modeling.
  • The DWM contributes to the ongoing development and comparative analysis within the field of cliodynamics.