2 papers
q-bio.NC2026
A Dynamical Blueprint for Brain State Organization
Kateryna Nechyporenko, Peter Ashwin, Krasimira Tsaneva-Atanasova
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…
math.DS2025
A Novel Route to Oscillations via non-central SNICeroclinic Bifurcation: Unfolding the Separatrix Loop Between a Saddle-Node and a Saddle
Kateryna Nechyporenko, Peter Ashwin, Krasimira Tsaneva-Atanasova
In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclini…