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Modular networks with delayed coupling: synchronization and frequency control.

Oleg V Maslennikov1, Vladimir I Nekorkin1

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Time delay in modular neural networks controls synchronization modes (in-phase and anti-phase) and network frequency. This study explores network dynamics across different topologies and coupling strengths.

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Area of Science:

  • Computational Neuroscience
  • Network Science
  • Systems Biology

Background:

  • Modular neural networks exhibit complex collective dynamics.
  • Map-based neurons generate irregular spike sequences, crucial for biological computation.
  • Understanding how network topology and delays influence synchronization is vital.

Purpose of the Study:

  • To investigate the collective dynamics of modular networks with varying intramodule topologies.
  • To analyze the role of time delays in synchrony and network oscillations.
  • To examine the impact of intermodule coupling strength and individual firing rates on synchronization.

Main Methods:

  • Simulating collective dynamics in modular networks with Erdös-Rényi, Watts-Strogatz, and Barabási-Albert topologies.
  • Introducing time-delayed sparse connections between modules.
  • Analyzing synchronization regimes (in-phase, anti-phase) and network frequency as a function of time delay.

Main Results:

  • Two synchronization regimes, in-phase and anti-phase, alternate with increasing time delay.
  • The average rate of collective oscillations decreases within each synchronization regime interval.
  • Time delay plays a dual role in controlling synchronization mode/degree and average network frequency.

Conclusions:

  • Time delay is a critical parameter for controlling both the mode and degree of synchronization in modular neural networks.
  • Network topology and intermodule coupling strength modulate the observed synchronization dynamics.
  • The findings offer insights into the principles governing information processing in complex, modular neural systems.