#### ** Upcoming Talk**

**Dec. 6 (Wed.)**** 14:00 - 15:00**
Alejandro López-Nieto (National Taiwan University)

Venue: Room 515, Cosmology Building (NTU Campus)

Title: *Periodic Solutions in Delay Equations with Monotone Feedback and Even-odd Symmetry*

Abstract:

Scalar delay differential equations (DDEs) of the form

$\dot{x}(t)=f(x(t),x(t−1))$,(1)

are used widely in real-world models that involve discrete-time lags. Such is the case inpopulation dynamics, where delays arise via maturation times, time-delayed feedback loops in laser devices, and heat transfer lags in atmospheric models. Mathematically, DDEs generate initial value problems in (infinite-dimensional) function spaces and often lead to complicated dynamics. However, the situation simplifies vastly under monotone feedback assumptions.

In the talk, I discuss the case when $f :{\mathbb{R}}^{2}\rightarrow \mathbb{R}$ in (1) is

● monotone in the delayed component, and

● possesses even-odd symmetry $f(\xi,\eta)=f(−\xi,\eta)=−f(\xi,−\eta)$.

The goal will be to show that all the periodic solutions of the DDE (1) arise as solutions to a boundary value problem in two dimensions (rather than infinite).