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math.DS2024
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…
math.DS2023
Transitions in echo index and dependence on input repetitions
Peter Ashwin, Andrea Ceni
The echo index counts the number of simultaneously stable asymptotic responses of a nonautonomous (i.e. input-driven) dynamical system. It generalizes the well-known echo state pro…