Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

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.