%0 Journal Article
%T Generate -Scroll Attractor via Composite Switching Controls
%A Baiyu Ou
%A Desheng Liu
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/414169
%X We propose a method for designing chaos generators. We introduce a switched system with three-dimensional space functions for generating a new type of chaotic attractor, and then we introduce saturated function series for generating -scroll chaotic attractor. Moreover, we present some examples with numerical simulations that illustrate the efficiency of our method. The statistic behavior is also discussed, which reveals the regularities in the complex dynamics. 1. Introduction Chaos is a very interesting nonlinear phenomenon, which has been extensively investigated during the last four decades. Since the 1960s, many chaotic (strange) attractors in dynamical systems have been found numerically and experimentally [1¨C3], such as Lorenz attractor [4], R£¿ssler attractor [5], and Chua¡¯s attractor [6¨C11]. This proved that pursuing systems that can exhibit chaos in form of chaotic attractors is very helpful in understanding complex behavior of nonlinear dynamical systems, and is especially important for chaos communication technology [12], in which a chaos generator is prerequisite for chaos communication. The Chua¡¯s circuit system that has double-scroll attractor is probably the best known and the simplest chaotic system that roots in a concrete physical system and has been extensively studied up to date [6, 13]. Moreover, multiscroll attractors are also found in some simple systems, to which nonlinear scalar functions, such as saturated function series [14] and switching scalar linear feedback [15], are implemented. Besides -scroll attractors, patterns of strange attractors, such as multiple stripes [16], and spherical pattern [17], have been constructed using simple structures. In [18], a chaotic attractor in a new funnel-shape is introduced, simply by designing a switched system with hysteresis switching signal. It also could be regarded as a method of chaotic attractor generation with one-dimensional space function. Motivated by this work, we introduce a switched system with three-dimensional space functions for generating a new type of chaotic attractor, and then we have made further effort to generate more chaotic behaviors, by introducing saturated function series, that is, a switched system with saturated function series approach is investigated. To our happiness, -scroll chaotic attractor is observed. And moreover, the attractor with funnel-shape is also emerged in each scroll. The statistic behavior is also discussed, which reveal the regularities in the complex dynamics. The rest of this paper is organized as follows. In Section 2, the concept of
%U http://www.hindawi.com/journals/mpe/2010/414169/