Running summarizing tools on a new article

Abstract: Introduction Spatio-temporal chaos is a feature of nonlinear spatially extended systems with large numbers of degrees of freedom, as described for instance by reaction–diffusion models of activator–inhibitor type. In this chapter we shall study a model system of this type that was introduced in Chapter 2 for layered semiconductor heterostructures, and used for a general analysis of pattern formation in Chapter 3. Here we shall investigate in detail the complex spatio-temporal dynamics including a codimension-two Turing–Hopf bifurcation, and asymptotic and transient spatio-temporal chaos. Chaos control of spatio-temporal spiking by time-delay autosynchronization is applied. The extensive chaotic state is characterized using Lyapounov exponents and a Karhunen–Loève eigenmode analysis. Spatio-temporal spiking in layered structures For understanding spatio-temporal chaos it is important to study first the elementary spatio-temporal patterns, which may eventually – in the course of secondary bifurcations – evolve into chaotic scenarios. One such elementary pattern, which has been observed experimentally in various different semiconductor devices exhibiting SNDC, e.g. layered structures such as p–n–p–i–n diodes (Niedernostheide et al . 1992 a ) and p–i–n diodes (Symanczyk et al . 1991 a ), or in impurity-impact-ionization breakdown (Rau et al . 1991, Spangler et al . 1992), and in electron–hole plasmas (Aliev et al . 1994), is the spiking mode of current filaments. The properties of localized spiking structures have been studied theoretically in detail by Kerner and Osipov (1982, 1989) in general reaction–diffusion systems. Spiking in a simple chemical reaction–diffusion model – the Brusselator – has been reported by De Wit et al . (1996).