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 n(x).
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).