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Coarse-Grained Clustering Dynamics of Heterogeneously Coupled Neurons

Journal Article · · The journal of mathematical neuroscience
 [1];  [2];  [2];  [2];  [3];  [4]
  1. Princeton University, NJ (United States); DOE/OSTI
  2. Princeton University, NJ (United States)
  3. Universidad de los Andes, Santiago (Chile)
  4. Massey University, Auckland (New Zealand)
+ Show Author Affiliations
The formation of oscillating phase clusters in a network of identical Hodgkin–Huxley neurons is studied, along with their dynamic behavior. The neurons are synaptically coupled in an all-to-all manner, yet the synaptic coupling characteristic time is heterogeneous across the connections. In a network of N neurons where this heterogeneity is characterized by a prescribed random variable, the oscillatory single-cluster state can transition—through (possibly perturbed) period-doubling and subsequent bifurcations—to a variety of multiple-cluster states. The clustering dynamic behavior is computationally studied both at the detailed and the coarse-grained levels, and a numerical approach that can enable studying the coarse-grained dynamics in a network of arbitrarily large size is suggested. Among a number of cluster states formed, double clusters, composed of nearly equal sub-network sizes are seen to be stable; interestingly, the heterogeneity parameter in each of the double-cluster components tends to be consistent with the random variable over the entire network: Given a double-cluster state, permuting the dynamical variables of the neurons can lead to a combinatorially large number of different, yet similar “fine” states that appear practically identical at the coarse-grained level. For weak heterogeneity we find that correlations rapidly develop, within each cluster, between the neuron’s “identity” (its own value of the heterogeneity parameter) and its dynamical state. For single- and double-cluster states we demonstrate an effective coarse-graining approach that uses the Polynomial Chaos expansion to succinctly describe the dynamics by these quickly established “identity-state” correlations. This coarse-graining approach is utilized, within the equation-free framework, to perform efficient computations of the neuron ensemble dynamics.
Research Organization:
Princeton Univ., NJ (United States) Dept. of Chemical and Biological Engineering and Program in Applied and Computational Mathematics
Sponsoring Organization:
Fondecyt grant; Marsden Fund Council; USDOE Office of Science (SC)
Grant/Contract Number:
SC0002120
OSTI ID:
1626690
Journal Information:
The journal of mathematical neuroscience, Journal Name: The journal of mathematical neuroscience Journal Issue: 1 Vol. 5; ISSN 2190-8567
Publisher:
SpringerOpenCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (5)

Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks journal October 2016
Coarse-Grained Descriptions of Dynamics for Networks with Both Intrinsic and Structural Heterogeneities journal June 2017
Cluster burst synchronization in a scale-free network of inhibitory bursting neurons journal July 2019
Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons posted_content April 2019
Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons preprint January 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
clustering dynamics
heterogeneous coupling
polynomial chaos expansion