Topological Method for Analysis of Periodic Canards1
A. A. Zhezherun∗,∗∗ and A. V. Pokrovskii∗,∗∗∗
∗University College Cork, Cork, Ireland
∗∗Samara State Regional Nayanova University, Samara, Russia
∗∗∗Institute for Information Transmission Problems, Moscow, Russia
Received August 4, 2008
Abstract—Singularly perturbed systems of ordinary differential equations are studied.
A method for analysis of canard-type trajectories in such systems based on the topological
degree theory is suggested. The method does not require smoothness of the right-hand side of
the system. A result on the existence of periodic canards in systems with non-smooth pertur-
bations is obtained. The trajectories located in this way are not necessarily Lyapunov stable,
and appropriate control algorithms are required to stabilize them, e.g., feedback control.
PACS number: 02.30.Yy