We kindly invite you to the Miklós Farkas Seminar
7 November (Thursday) 10.15, BME, H306
Gabriella Vas (MTA-SZTE Analysis and Stochastics Research Group, Bolyai Institute, University of Szeged)
Large-amplitude periodic orbits for delay equations
Let us consider scalar delay differential equations of the form x'(t)=-ax(t)+f(x(t-1)), where a>0 and f is a nondecreasing C1-function. This talks gives an overview of the periodic orbits and the global attractor.
After showing some well-known results of Tibor Krisztin, Hans-Otto Walther and Jianhong Wu, I introduce the notion of large-amplitude periodic (LAP) orbits. First we discuss the bifurcation and the existence of a pair of LAP orbits. Then we describe the geometric properties of the unstable set of a specific LAP orbit in detail. Complicated configurations of LAP orbits appear when the dynamical system has several unstable equilibria – we also consider this case. These are joint works with Tibor Krisztin and Szandra Beretka.
No preliminary knowledge of delay equations is presumed.
(István Faragó, János Karátson, Róbert Horváth, Miklós Mincsovics, Gabriella Svantnerné Sebestyén)
Visit the homepage of the seminar: http://math.bme.hu/AlkAnalSzemi