On Friday (March 6), at 6:00 PM, Ilya Fateev (Lebedev Physical Institute) will present a paper titled "Partial Synchronization States in Neuronal Systems with Superdiffusion Coupling" (the paper will be based on Ilya's dissertation).
Abstract: This paper will present the results of a study of the dynamics of partial synchronization in neuronal ensembles. A key feature of the model under consideration is the superdiffusion nature of the connections between elements, based on a difference scheme for approximating the fractional Laplace operator.
The paper will discuss the neuroscientific motivation for this work, namely, the conceptual alignment of the proposed mathematical formulation with modern understanding of the structural and functional properties of cortical structures. Attention will also be paid to the analysis of the continuous limit of a discrete neural network, which leads to a reactive-superdiffusion representation.
Specifically, the paper will present results linking the types of spatial mode stability with dynamic regimes of complete and partial synchronization, as well as developed incoherence in a discrete system. It will be demonstrated how the parametric space of exponents of the fractional Laplace operator (which determines the architecture of superdiffusion interaction) defines scenarios for the transition from spatial disorder to spatiotemporal organization.