Enhanced delay to bifurcation and canard cycles in slow-fast systems
by
Jean Pierre Francoise(Paris, Jussieu)
→
Europe/Rome
Aula Conversi (Dip. di Fisica - Edificio G. Marconi)
Aula Conversi
Dip. di Fisica - Edificio G. Marconi
Description
Fast-slow dynamical systems are often studied by geometrical dissection. The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics, seen as a parameter of the fast dynamics. A generic solution comes close to a connected component of the stable invariant sets of the fast dynamics. As the slow dynamics evolves, this attractor may lose its stability and the solution eventually jumps to another connected component of attractors of the fast dynamics and the process may repeat. This scenario explains quite well relaxation oscillations and more complicated oscillations like bursting. This talk will be devoted to the analysis of several meaningful counterexamples. The basic idea relates to a delay to the bifurcation associated to a defect of hyperbolicity of the slow manifold. There is even a possibility of enhanced delay combined with a recurrence.
