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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.
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Shirley Carr
reviewed The 2-dimensional attractor of x(t)=-[mu]x(t)+f(x(t-1)) on September 03, 2018![3 Stars Rating for The 2-dimensional attractor of x(t)=-[mu]x(t)+f(x(t-1)), , The 2-dimensional attractor of x(t)=-[mu]x(t)+f(x(t-1))](https://WonderClub.com/images/stars-3-0.gif)
The 2-dimensional attractor of x
Every few years I take this book out and reread it. Yolen writes with deceptive simplicity and clarity that one doesn't realize how profoundly true her words are until they keep coming back in memory.
From this book comes a (deservedly) repeated quotation, which I reproduce here, as I use it frequently to give the short answer why I can't read game of Thrones, well-written as it is:
And for adults, the world of fantasy books returns to us the great words of power which, in order to be tamed, we have excised from our adult vocabularies. These words are the pornography of innocence, words which adults no longer use with other adults, and so we laugh at them and consign them to the nursery, fear masking as cynicism. These are the words that were forged in the earth, air, fire, and water of human existence, and the words are:
Love. Hate. Good. Evil. Courage. Honor. Truth."
And:
"Touch magic. Pass it on."
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