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This study models financial markets using a novel network system to analyze repeated buying and selling cascades. The research identifies critical network conditions influencing market dynamics and provides a framework for understanding agent behavior.

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Area of Science:

  • Complex Systems Science
  • Network Dynamics
  • Computational Finance

Background:

  • Existing research often overlooks dynamic processes in networks with repeated, opposing cascades.
  • Financial markets exhibit such phenomena, with rapid buying and selling cascades occurring frequently.
  • Understanding these dynamics is crucial for financial market stability and agent behavior analysis.

Purpose of the Study:

  • To develop and analyze a model for networks exhibiting repeated cascades of opposing influence.
  • To investigate the dynamical behavior of financial markets using a stochastic pulse-coupled oscillator network.
  • To identify conditions governing asynchronous and synchronous regimes and predict cascade sizes.

Main Methods:

  • A stochastic pulse-coupled oscillator network model with upper and lower thresholds was developed.
  • Numerical simulations were used to confirm asynchronous and synchronous operational regimes.
  • Analytical methods identified the fixed point state vector for the asynchronous mean field system.

Main Results:

  • The study analytically identified a lower bound for network coupling probability separating asynchronous and synchronous regimes.
  • A closed-form equation for cascade size was derived for the low-dimensional mean field system.
  • The model successfully captures key features of financial market dynamics.

Conclusions:

  • The developed network model provides a robust framework for studying systems with repeated opposing cascades.
  • The findings offer insights into the critical network coupling probabilities influencing market behavior.
  • The model has direct applicability to understanding interacting agent dynamics in financial markets.