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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Systems Biology

Background:

  • Phase synchronization is crucial in coupled oscillator systems.
  • Amplitude dynamics can influence synchronization but is often neglected.
  • Understanding synchronization in random complex networks is challenging.

Purpose of the Study:

  • To investigate how amplitude dynamics affects phase synchronization in random complex networks.
  • To compare synchronization in systems with and without amplitude dynamics.
  • To determine the impact of network topology and node frequency distribution.

Main Methods:

  • Studied coupled periodic oscillators with and without amplitude dynamics.
  • Compared heterogeneous units (amplitude and phase) with pure phase oscillators (Kuramoto model).
  • Analyzed small network motifs and random complex network topologies.
  • Investigated coupled FitzHugh-Nagumo units near Hopf bifurcations.

Main Results:

  • Amplitude dynamics can enhance phase synchronization, especially when not negligible.
  • Synchronization behavior depends on network topology and node frequency distribution.
  • Abundant microscopic structures in random networks benefit from amplitude dynamics.
  • Amplitude dynamics generally lowers the synchronization threshold in random topologies.
  • Synchronization enhancement is observed in oscillators near Hopf bifurcations.

Conclusions:

  • Amplitude dynamics plays a significant role in enhancing phase synchronization in complex networks.
  • The findings suggest a general mechanism for improved synchronization across various random network structures.
  • The study provides insights into neuronal dynamics and synchronization near Hopf bifurcations.