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Synchronization in networks with heterogeneous coupling delays.

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This study analyzes synchronization in networks with varied coupling delays using a new operator. Increased delay heterogeneity expands instability regions for synchronized spiking in neural networks.

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Area of Science:

  • Complex systems
  • Network dynamics
  • Computational neuroscience

Background:

  • Synchronization is crucial in many natural and engineered systems.
  • Coupling delays significantly impact network synchronization.
  • Existing methods often assume homogeneous delays, limiting applicability.

Purpose of the Study:

  • To develop a generalized method for analyzing synchronization in networks with heterogeneous coupling delays.
  • To extend the master stability function approach to systems with non-uniform delays.
  • To investigate the impact of delay heterogeneity on network stability.

Main Methods:

  • Introduced an adjacency lag operator to decompose network dynamics.
  • Utilized block diagonalization for analyzing network topology and delays.
  • Applied frequency domain methods for stability analysis of synchronized states.
  • Investigated delay-coupled Hodgkin-Huxley neurons as a case study.

Main Results:

  • The network dynamics can be analyzed using delay differential equations with distributed delays.
  • Different delay distributions arise for different network modes.
  • Increasing delay heterogeneity expands the parameter regions where synchronized periodic spiking is unstable.

Conclusions:

  • The generalized approach effectively analyzes synchronization in networks with heterogeneous delays.
  • Delay heterogeneity plays a critical role in the stability of synchronized states.
  • Findings have implications for understanding complex systems, particularly neural networks.