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From Chaos to Coherence: Effects of High-Order Synaptic Correlations on Neural Dynamics
Nimrod Sherf1,2, Xaq Pitkow2,3,4,5,6, Krešimir Josić1,7
1Department of Mathematics, University of Houston, Houston, Texas, USA.
Arxiv
|September 15, 2025
Summary
High-order cyclic correlations in synaptic connectivities significantly impact neuronal network dynamics. Strong correlations suppress chaotic activity, promoting stable, rhythmic patterns in the brain.
Area of Science:
- Computational neuroscience
- Network science
- Systems biology
Background:
- Recurrent Neural Network (RNN) models illuminate biological neural network dynamics, particularly cortical activity patterns.
- Existing research primarily examines random or simple network connectivity, overlooking complex structures.
- Experimental data suggest high-order connectivity influences temporal activity, yet a theoretical framework is lacking.
Purpose of the Study:
- To investigate the impact of third- and higher-order cyclic correlations in synaptic connectivities on neuronal network dynamics.
- To develop a theoretical understanding linking complex network structures to emergent dynamics.
- To explore how specific connectivity patterns influence the transition between chaotic and stable activity.
Main Methods:
- Analysis of RNN models with varying orders of cyclic correlations in synaptic connectivities.
- Examination of the relationship between network structure, eigenvalue spectra of connectivity matrices, and emergent dynamics.
- Investigation of phase transitions from chaotic to fixed or oscillatory activity.
Main Results:
- Third- and higher-order cyclic correlations in synaptic connectivities significantly alter neuronal dynamics.
- Strong cyclic correlations suppress chaotic dynamics, favoring oscillatory or fixed activity states.
- A phase transition from chaotic to stable dynamics is associated with a cusp formation in the eigenvalue support.
- The dimensionality of network activity is demonstrably linked to the underlying network structure.
Conclusions:
- High-order cyclic correlations are critical determinants of neuronal network dynamics, moving beyond simple connectivity models.
- The presence of strong cyclic correlations can stabilize neural activity, preventing chaotic states.
- Eigenvalue analysis provides a theoretical basis for understanding structure-dynamics relationships and predicting activity transitions.
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