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math.DS2026
Local interaction of two systems with saddle-node bifurcations: mutualistic and mixed cases
Peter Ashwin, Claire Postlethwaite, Jan Sieber
The saddle-node bifurcation is the simplest example of a generic bifurcation in smooth ordinary differential equations, and is associated with the creation or destruction of a pair…
math.DS2025
Alpha-Delta Transitions in Cortical Rhythms as grazing bifurcations
Huda Mahdi, Jan Sieber, Krasimira Tsaneva-Atanasova
The Jansen-Rit model of a cortical column in the cerebral cortex is widely used to simulate spontaneous brain activity (EEG) and event-related potentials. It couples a pyramidal ce…