Research

• My research is focused on geometric singular perturbation theory and the canard phenomenon in the context of both smooth and non-smooth (Filippov, piecewise-linear) dynamical systems. I am looking at the robustness of slow-fast phenomena in general, and canard behaviours in particular.
  Collaborators: Mike Jeffrey (University of Bath, UK), John Hogan (University of Bristol), Phani Thota (Airbus Industry, UK), Enrique Ponce (University of Sevilla, Spain).


• As a related independent research, I am interested in applications of multiple timescale dynamics in biology and neuroscience, e. g., complex oscillatory and canard phenomena in neuronal and bursting models (mixed-mode oscillations in Hodgkin-Huxley type models, spike-adding mechanisms via saddle-type canards in square-wave bursters). In particular, I am studying a new type of canard behaviour related to bursting and which takes place during the fast part of the dynamics; it has been termed torus canard.
  Collaborators: John Burke, Tasso Kaper and Mark Kramer (Boston University, USA).


• Finally, I am working on further developments of numerical continuation methods adapted to the study of multiple time scale dynamics and to the computation of challenging dynamical objects (invariant manifolds, isolas, complex i.e. multi-mode oscillations).
  Collaborators: Daniele Avitabile (University of Nottingham, UK) and Serafim Rodrigues (University of Plymouth, UK)