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Mean-field approximation for networks with synchrony-driven adaptive coupling.

N Fennelly1, A Neff2, R Lambiotte3

  • 1School of Mathematics and Statistics, University College Dublin, Dublin 4 D04 V1W8, Ireland.

Chaos (Woodbury, N.Y.)
|January 27, 2025
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Summary
This summary is machine-generated.

This study introduces adaptive plasticity to neuron models, revealing new dynamics like bistability and chaos. These complex behaviors arise from phase-difference-dependent plasticity rules in coupled θ-neuron oscillators.

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Area of Science:

  • Computational neuroscience
  • Theoretical neuroscience
  • Complex systems

Background:

  • Synaptic plasticity is crucial for neuronal dynamics and learning.
  • Existing models often use complex spike-timing-dependent plasticity (STDP).
  • Adaptive plasticity offers a more tractable approach to model neuronal network evolution.

Purpose of the Study:

  • To incorporate adaptive plasticity into a network model of θ-neuron oscillators.
  • To investigate the impact of phase-difference-dependent plasticity on neuronal synchrony and dynamics.
  • To analyze the emergence of complex behaviors like bistability and chaos.

Main Methods:

  • Utilized a network model of θ-neuron oscillators.
  • Implemented pairwise and global updates for phase-difference-dependent plasticity.
  • Derived and validated a mean-field approximation against simulations.
  • Employed bifurcation analysis and Lyapunov exponents to characterize system dynamics.

Main Results:

  • The adaptive plasticity model exhibits bistability and chaotic dynamics.
  • Period-doubling and boundary crisis bifurcations were observed.
  • These phenomena are absent in systems lacking adaptive coupling.
  • The mean-field approximation accurately reflects simulation results across stability regimes.

Conclusions:

  • Adaptive phase-difference-dependent plasticity significantly alters neuronal network dynamics.
  • The model provides insights into the emergence of complex behaviors in neural systems.
  • This approach offers a simplified yet powerful framework for studying synaptic plasticity.