SearcharxivSearch

arXiv subjects

Kateryna Nechyporenko

Publications and source records attributed to Kateryna Nechyporenko.

2 recordsLinked to original sources

A Dynamical Blueprint for Brain State Organization

The brain is not static: neuronal networks shift between contrasting modes of activity, alternating between active and quiescent regimes known as up and down states. Together with rhythmic oscillations, such modes of activity are fundamental to perception, memory, and information processing. However, the dynamical principles underlying the diverse repertoire of activity patterns and their transitions remain poorly understood. Here, we identify a geometric structure that governs dynamic states emergence and organizes neuronal networks transitions. We derive the conditions for its existence and demonstrate that it emerges robustly across canonical models of neuronal population dynamics. Near this organizing center, switches between oscillations, bistability and up and down states are orchestrated by the excitation-inhibition balance in the neuronal network. Thus, we show that excitation and inhibition do not simply modulate network activity but define the dynamical landscape from which distinct brain states emerge. We also consider neuron-astrocyte interactions and reveal how astrocytes can tune excitatory-inhibitory balance, therefore modulating the transitions between neuronal activity regimes. Overall, our results identify a general dynamical blueprint underlying the emergence, organization, and control of brain states.

q-bio.NC

A Novel Route to Oscillations via non-central SNICeroclinic Bifurcation: Unfolding the Separatrix Loop Between a Saddle-Node and a Saddle

In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle. A particular codimension-three case is the non-central SNICeroclinic bifurcation. We unfold this bifurcation in the minimal dimension (planar) case where the non-hyperbolic point is assumed to undergo a saddle-node bifurcation. Applying the method of Poincaré return maps, we present a minimal set of perturbations that captures all qualitatively distinct behaviors near a non-central SNICeroclinic loop. Specifically, we study how variation of the three unfolding parameters leads to transitions from heteroclinic and homoclinic loops, saddle-node on an invariant circle (SNIC), and periodic orbits as well as equilibria. We show that although the bifurcation has been largely unexplored in applications, it can act as an organizing center for transitions between various types of saddle-node and saddle separatrix loops. It is also a generic route to oscillations that are both born and destroyed via global bifurcations, compared to the commonly observed scenarios involving local (Hopf) and in some cases global (homoclinic or SNIC) bifurcations.

math.DS