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Adaptive coupling in neural networks can lead to complex behaviors like synchronization and chaos. This study analyzes how adaptivity in coupling strength influences the dynamics of two Theta neurons, revealing new insights into network behavior.

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Network Science

Background:

  • Coupled oscillators and neuronal networks display complex cooperative dynamics, crucial for phenomena like brain activity and power grid stability.
  • Co-evolutionary networks, with dynamics on and of the network across mixed time scales, are a growing area of interest.

Purpose of the Study:

  • To investigate the collective behavior of two adaptive coupled Theta neurons without self-interaction.
  • To understand how varying levels of adaptivity in coupling strength influence network dynamics using bifurcation analysis and simulations.

Main Methods:

  • Bifurcation analysis to identify stability regions and dynamics.
  • Numerical simulations to explore the effects of adaptive coupling strength (a).

Main Results:

  • In the non-adaptive limit, bifurcation analysis revealed stable regions of quiescence and spiking with various mode-locking configurations.
  • Increasing adaptivity (a) widened Arnold tongues, leading to multi-stable configurations and potential period-doubling cascades into chaos.

Conclusions:

  • The level of adaptivity in coupling strength significantly shapes the collective dynamics of neural networks.
  • Findings offer insights into neuronal communication, synchronization mechanisms, and the mathematical theory of adaptive networks.