Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
Periodic Solutions in Delay Equations with Monotone Feedback and Even-odd Symmetry
Alejandro López-Nieto (National Taiwan University)
Abstract
Scalar delay differential equations (DDEs) of the form
%3Df(x(t)%2Cx(t-1))&chf=bg,s,333333&chco=ffffff)
, (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
in (1) is
• monotone in the delayed component, and
• possesses even-odd symmetry %3Df(-%5Cxi%2C%5Ceta)%3D-f(%5Cxi%2C-%5Ceta)%24&chf=bg,s,333333&chco=ffffff)
.
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).
