Topological markers of dynamical regimes in spiking neural networks

Understanding the complex dynamics of neural networks is crucial for unraveling the mechanisms underlying brain functioning. In this study, we approach the issue of synchrony in the collective behavior of neurons from a topological perspective, employing the machinery of principal component analysis (PCA), persistent homology (PH), and the embedding dimension. Using the Morris-Lecar neural model as an example, we demonstrate how these instruments can be applied to the data of activity of a spiking neural network to characterize its dynamic regime. We show that topological data analysis (TDA) of neural activity can serve as an effective mean of neurodynamic inquiry and provide new insights into the function of neural networks. Thereby, this work motivates further research on the application of topological methods to the problems of neural dynamics.