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Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons.

Sung Joon Moon1, Katherine A Cook1, Karthikeyan Rajendran1

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Oscillating phase clusters form in networks of Hodgkin-Huxley neurons with heterogeneous synaptic coupling. These clusters transition to multiple states, with stable double clusters emerging and showing identity-state correlations useful for coarse-graining dynamics.

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Area of Science:

  • Computational neuroscience
  • Complex systems dynamics
  • Nonlinear dynamics

Background:

  • Hodgkin-Huxley neurons are fundamental models of neuronal excitability.
  • Heterogeneous synaptic coupling can lead to complex network dynamics.
  • Understanding emergent network states is crucial in neuroscience.

Purpose of the Study:

  • To investigate the formation and dynamics of oscillating phase clusters in a network of Hodgkin-Huxley neurons.
  • To analyze the transition from single-cluster to multiple-cluster states.
  • To develop and apply a coarse-graining method for large-scale neural network simulations.

Main Methods:

  • Simulating networks of all-to-all coupled Hodgkin-Huxley neurons with heterogeneous synaptic coupling times.
  • Analyzing detailed and coarse-grained dynamics using computational approaches.
  • Employing Polynomial Chaos expansion for an effective coarse-graining strategy within an equation-free framework.

Main Results:

  • Oscillatory single-cluster states transition to multiple-cluster states via period-doubling bifurcations.
  • Stable double-cluster states emerge, with component subnetworks showing consistent heterogeneity parameters.
  • Rapid development of correlations between neuron identity (heterogeneity parameter) and dynamical state within clusters for weak heterogeneity.

Conclusions:

  • Heterogeneous synaptic coupling drives complex clustering dynamics in neural networks.
  • A coarse-graining approach using Polynomial Chaos expansion effectively captures network dynamics by leveraging identity-state correlations.
  • This method enables efficient computation of large-scale neuron ensemble dynamics.