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Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
Synchronizing Hindmarsh-Rose neurons over Newman-Watts networks.
1Department of Computer Engineering, Sharif University of Technology, Tehran, Iran. mjalili@sharif.edu
Chaos (Woodbury, N.Y.)
|October 2, 2009
Summary
Researchers studied how Hindmarsh-Rose neuron models synchronize on Newman-Watts networks. Synchronization strength depends on network structure, with clustered networks showing power-law relationships influenced by intercluster connection probability.
Area of Science:
- Computational Neuroscience
- Network Science
- Complex Systems
Background:
- The Hindmarsh-Rose neuron model is a mathematical model of bursting electrical activity in neurons.
- Newman-Watts networks are a class of random graphs that exhibit small-world properties.
- Understanding synchronization in neural networks is crucial for deciphering brain function and dysfunction.
Purpose of the Study:
- To investigate the synchronization behavior of Hindmarsh-Rose neuron models on Newman-Watts networks.
- To determine the uniform synchronizing coupling strength using numerical and analytical methods.
- To analyze the impact of network topology, neuron identity, and coupling types on synchronization.
Main Methods:
- Numerical solution of the network's differential equations.
- Application of the master-stability-function method.
- Analysis of synchronization error for non-identical neurons.
- Investigation of clustered Newman-Watts networks and combined electrical/chemical coupling.
Main Results:
- The gap between numerically obtained and master-stability-function-derived coupling strengths increases with average degree.
- This gap is independent of network size for the studied network class.
- For large networks, synchronizing strength follows a power-law with shortcut probability.
- Synchronization in clustered networks is primarily influenced by intercluster connection probability via a power-law relationship.
Conclusions:
- Network topology significantly impacts neural synchronization, with specific features like shortcut probability and clustering playing key roles.
- The master-stability-function method provides insights into synchronization but diverges from numerical results as average degree increases.
- Combined electrical and chemical coupling can enhance complete synchronization in neural networks.
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