Metric framework of coherent activity patterns identification in spiking neuronal networks

Chaos, Solitons and Fractals. 2026. Vol. 203. Article 117645.

Daniil Radushev, Dogonasheva O., Gutkin B., Zakharov D.

The formation of coherent activity patterns in neuronal populations presents challenges to synchronization theory. These patterns
are often involved in cognitive tasks and typically last for short durations [2,3]. Furthermore, they do not involve all neurons in
the network, but only the subsets required for specific computations.
Numerous approaches exist to classify synchronous regimes in neuronal networks using numerical parameters — or combinations
of them — that characterize the network’s global state [10–14,18,22,23]. However, these tools provide only a rough description
of the network state and do not offer information about the localization or specific properties of distinct activity patterns. To
facilitate more detailed investigation of neuronal network dynamics, there is a need for methods that focus on the characterization
of individual patterns rather than the aggregated evaluation of the entire network.
In this paper, we introduce the Metric Framework (MF)—a novel approach to neuronal network activity analysis that enables
the automatic localization and description of distinct coherent activity patterns at a given moment in time. This approach interprets
the network as a metric space of neurons accompanied with an Activity Function (AF), which maps each neuron to its activity
characteristic (e.g., membrane potential, spike phase) at a fixed time point 𝑡0.
Coherent clusters are defined as regions where the AF changes continuously with respect to the network’s spatial structure,
while abrupt changes in AF indicate incoherent regions. Within each coherent cluster, we analyze the analytic properties of the AF
to determine the specific type of coherence it represents (e.g., synphase synchrony, traveling wave). In this way, the MF provides
precise localization and characterization of coherent activity patterns.

Keywords: метрическое пространство, химерное состояние, спайковые нейронные сети, chimera states, синхронные кластеры, Partial synchronization, частичная синхронизация, Spiking neuronal network, Activity patterns, Metric space, Synchronous clusters

Publication based on the results of: Multidisciplinary study of behavior and decision-making in health population and patients using behavioral, economic, neurocognitive, neuroeconomic, neurocomputational and neural network approaches (2025)