Explicit maps to predict activation order in multiphase rhythms of a coupled cell network.

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Systems Neuroscience

Background:

• Neuronal network models are crucial for understanding complex biological rhythms.
• Fast-slow dynamics offer insights into the temporal organization of neural activity.
• Heterogeneity in neuronal intrinsic dynamics can significantly alter network behavior.

Purpose of the Study:

• To extend fast-slow analysis for coupled networks of three heterogeneous cells.
• To develop analytical tools for predicting cell activation patterns.
• To investigate the impact of cell heterogeneity on network dynamics.

Main Methods:

• Utilized a novel extension of fast-slow analysis for coupled neuronal networks.
• Modeled each cell with pairs of first-order differential equations (fast and slow variables).
• Derived explicit maps between slow variables to predict activation orders.

Main Results:

• Developed analytical maps to determine cell activation sequences in heterogeneous networks.
• Showed how these maps constrain possible activation orders based on initial conditions.
• Created a unified 2D map to analytically derive boundary curves for different activation patterns.

Conclusions:

• The developed fast-slow analysis provides a powerful tool for predicting dynamics in complex neuronal networks.
• Heterogeneity can be systematically incorporated into network models to reveal diverse activation patterns.
• This approach offers a pathway to analytically understand and predict emergent network behaviors.