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This study introduces a data-driven simulation method for complex systems. It successfully models business firm evolution, revealing universal scaling laws and consistent fluctuation distributions.

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Area of Science:

  • Complex Systems Science
  • Computational Economics
  • Statistical Physics

Background:

  • Simulating the long-term evolution of complex systems often requires detailed knowledge of underlying dynamics.
  • Existing methods may struggle with high-dimensional data and lack of complete system information.
  • Understanding business firm evolution and its scaling properties is crucial for economic analysis.

Purpose of the Study:

  • To propose and validate a novel data-driven stochastic method for simulating complex system evolution.
  • To apply the method to a large dataset of business firm trajectories over 25 years.
  • To investigate the emergence of scaling laws and fluctuation distributions in business firm size.

Main Methods:

  • Developed a stochastic simulation approach utilizing historical trajectory data.
  • Employed random selection of partial trajectories without explicit system dynamics.
  • Applied the method to a dataset of approximately one million business firms over a quarter century.

Main Results:

  • Achieved a stationary distribution in a three-dimensional log-size phase space from simulations.
  • Demonstrated that the obtained distribution satisfies allometric scaling laws for three variables.
  • Observed universal fluctuation distributions around scaling relations, consistent with empirical data.

Conclusions:

  • The proposed data-driven method effectively simulates complex system evolution.
  • The study reveals emergent allometric scaling laws in business firm size distributions.
  • The findings support the universality of fluctuation patterns in complex economic systems.