The 2-Dimensional Attractor of X' (Memoirs of the American Mathematical Society) by Hans-Otto Walther
The 2-Dimensional Attractor of X' (Memoirs of the American Mathematical Society)
Author: Hans-Otto Walther
Title: The 2-Dimensional Attractor of X' (Memoirs of the American Mathematical Society)
ISBN10: 0821826026
ISBN13: 978-0821826027
Format: .PDF .EPUB .FB2
Pages:
Publisher: Amer Mathematical Society (March 1, 1995)
Language: English
Size pdf: 1526 kb
Size epub: 1247 kb
Rating: 4.1 ✪
Votes: 366
Category: Other
Subcategory: Science & Mathematics
The equation $x'(t) = - mu x(t) + f(x(t-1))$, with $mu geq 0$ and $xf(x) le 0$ for $0neq xin {mathbb R}$, is a prototype for delayed negative feedback combined with friction. Its semiflow on $C=C([-1,0],{mathbb R})$ leaves a set $S$ invariant, which also plays a major role for the dynamics on the full space $C$. The main result determines the attractor of the semiflow restricted to the closure of $S$ for monotone, bounded, smooth $f$. In the course of the proof, Walther derives Poincaré-Bendixson theorems for differential-delay equations. The method used here is unique in its use of winding numbers and homotopies in nonconvex sets.