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).
