Recurrence quantification analysis for the identification of burst phase synchronisation.

Area of Science:

• Computational Neuroscience
• Complex Systems Analysis
• Network Science

Background:

• Chaotic bursting neurons are crucial in neural dynamics.
• Understanding phase synchronization in complex neural networks is challenging.
• Existing methods may not fully capture spatial synchronization patterns.

Purpose of the Study:

• To apply spatial recurrence quantification analysis (RQA) for identifying chaotic burst phase synchronization.
• To analyze synchronization in a single small-world neural network and a network of small-world subnetworks.
• To determine the capability of spatial RQA in detecting synchronized neuron groups and their sizes.

Main Methods:

• Utilized the Rulkov map to model chaotic bursting neuron dynamics.
• Employed spatial recurrence quantification analysis (RQA) on network structures.
• Derived an analytical expression for spatial recurrence rate using Gaussian approximation for single networks.
• Investigated clustered networks composed of small-world subnetworks.

Main Results:

• Spatial RQA successfully identified groups of synchronized neurons and quantified their sizes.
• An analytical expression for spatial recurrence rate was obtained for single networks.
• Phase synchronization within and between subnetworks was identified in clustered networks.
• Demonstrated the effectiveness of spatial RQA in complex network topologies.

Conclusions:

• Spatial RQA is a powerful tool for detecting and analyzing chaotic burst phase synchronization in neural networks.
• The method is applicable to both single complex networks and networks of networks.
• Spatial RQA provides insights into the spatial organization of synchronized neuronal activity.