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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Stuart-Landau oscillators are fundamental models for studying synchronization phenomena.
  • Hierarchical network organization introduces complexity in system dynamics.
  • Activity-dependent couplings and network motifs significantly influence oscillator behavior.

Purpose of the Study:

  • To investigate the global synchronization of hierarchically organized Stuart-Landau oscillator networks.
  • To explore the relationship between local network motifs, phase attractors, and global synchronization.
  • To determine how local complexity influences the controllability of global synchronization.

Main Methods:

  • Modeling hierarchically organized Stuart-Landau oscillators with activity-dependent couplings.
  • Analyzing all possible coupling signs within subsystems to identify network motifs.
  • Investigating subsystem coupling through mean oscillator activities.
  • Examining the correlation between the number of attractors in uncoupled subsystems and inter-subsystem synchronization under weak coupling.

Main Results:

  • Different network motifs within subsystems generate varying numbers of phase attractors.
  • The number of phase attractors in uncoupled subsystems strongly correlates with inter-subsystem synchronization under weak coupling.
  • Perfect anti-symmetric network motifs uniquely produce both single and multiple attractors based on oscillator activity.
  • Flexible local complexity offers a mechanism for controlling global synchronization.

Conclusions:

  • The number of phase attractors within subsystems is a critical determinant of global synchronization in hierarchically organized networks.
  • Network motif design within subsystems allows for the tuning of local complexity.
  • This tunable local complexity provides a pathway to control the global synchronization behavior of the entire system.