The 2-Dimensional Attractor of X' (Memoirs of the American Mathematical Society) by Hans-Otto Walther

**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

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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.