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Stability analysis and synchronization in discrete-time complex networks with delayed coupling.

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This study introduces a new network model where intra-neural communication has delays. We found that more connections and odd delays improve network synchronization, enhancing synchronizability compared to prior models.

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Area of Science:

  • Complex Systems and Network Science
  • Computational Neuroscience
  • Dynamical Systems Theory

Background:

  • Previous research (Atay et al., 2004) focused on inter-neural communication delays.
  • Understanding synchronization in coupled map networks is crucial for information processing.
  • Network topology and coupling strength influence system dynamics.

Purpose of the Study:

  • To propose a novel network of coupled maps with intra-neural delays.
  • To investigate the impact of delays, coupling strength, and network topology on synchronization.
  • To compare the synchronizability of the proposed model with existing frameworks.

Main Methods:

  • Development of a new coupled map network model incorporating intra-neural delays.
  • Analysis of synchronization based on intrinsic dynamics, graph Laplacian spectrum, delays, and coupling strength.
  • Comparative analysis with the model proposed by Atay et al. [Phys. Rev. Lett. 92, 144101 (2004)].

Main Results:

  • Network synchronization is influenced by intrinsic dynamics, topology, delays, and coupling strength.
  • Increased number of neighbors facilitates easier synchronization.
  • Odd delays promote synchronization more effectively than even delays.

Conclusions:

  • The proposed network model demonstrates improved synchronizability, particularly for regular and small-world networks.
  • Intra-neural delays play a significant role in network synchronization dynamics.
  • Network structure and delay characteristics are key determinants of synchronization efficiency.