Dr. Chiara Zanini
(Dipartimento di Matematica e Informatica, Università di Udine, Italy)
Periodic solutions and complex dynamics for a differential equation
arising in the study of a nerve fiber model
We deal with the periodic boundary value problem for a second-order
nonlinear ODE which includes the case of the Nagumo type equation
vxx - g v + n(x) F(v) = 0, previously considered by Chen and Bell in
the study of nerve fiber models.
We discuss the case of nonexistence of nontrivial solutions as well as the
case in which many positive periodic solutions may arise, the different
situations depending by threshold parameters related to the weight function
We also show that for some weight functions it is possible to obtain
infinitely many periodic solutions and chaotic dynamics, due to the presence of
a topological horseshoe.
This is joint work with Fabio Zanolin from University of Udine (Italy).