Nonlinear feedback systems with memory: From 0th to higher order, discrete and continuous (Q2738683)

The author discusses the various and rich dynamical behavior and its relationship in several classes of difference, differential, and differential delay equations. The classes include the one-dimensional discrete equation NEWLINE\[NEWLINE x_n=f(x_{n-1}),\quad f:\mathbb{R}\rightarrow \mathbb{R},\quad n\in \mathbb{N},NEWLINE\]NEWLINE and its analog, the equation with continuous argument \(t\), NEWLINE\[NEWLINE x(t)=f(x(t-1)),\quad t\in \mathbb{R}_+, NEWLINE\]NEWLINE the model of Goodwin oscillators with delay NEWLINE\[NEWLINE dx_1(t)/dt=f(x_k(t-\tau))-\alpha x_1(t),\quad dx_i(t)/dt=\alpha x_{i-1}(t)-\alpha x_i(t), i=2,3,\dots,k, NEWLINE\]NEWLINE the well known Mackey-Glass equation NEWLINE\[NEWLINE \varepsilon dx(t)/dt=f(x(t-1))-x(t), NEWLINE\]NEWLINE and some of their discrete versions. The paper is of review nature and is based on previously published results.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00044].