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System size synchronization.

María Laura Olivera-Atencio1, Manuel Morillo1, Jesús Casado-Pascual1

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Summary
This summary is machine-generated.

This study reveals system size synchronization in complex systems. Synchronization occurs when output frequency locks to external input and phase diffusion minimizes across specific system sizes.

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Area of Science:

  • Complex Systems Dynamics
  • Stochastic Processes
  • Nonlinear Dynamics

Background:

  • Complex systems often exhibit emergent behaviors not present in individual units.
  • Understanding synchronization phenomena is crucial for various scientific disciplines.
  • Externally driven stochastic systems present unique challenges in analyzing collective behavior.

Purpose of the Study:

  • To investigate a novel synchronization phenomenon related to the size of a complex system.
  • To define and analyze system size synchronization in externally driven stochastic systems.
  • To establish the conditions under which system size synchronization occurs.

Main Methods:

  • Construction of a dichotomic random jump process for N coupled units.
  • Definition of output frequency and phase diffusion coefficients.
  • Application of analytical and numerical procedures to study the phenomenon.

Main Results:

  • System size synchronization is identified as a distinct phenomenon.
  • Synchronization is characterized by output frequency locking to the external frequency.
  • A deep minimum in average phase diffusion coefficient is observed for specific system sizes.

Conclusions:

  • The study successfully demonstrates the existence of system size synchronization.
  • The findings provide a new perspective on how system size influences collective dynamics.
  • This research offers a framework for understanding synchronization in complex stochastic systems.