Experimental verification of multidirectional multiscroll chaotic attractors

Abstract

A systematic methodology for circuit design is proposed for experimental verification of multidirectional multiscroll chaotic attractors, including one-directional (1-D) n-scroll, 2-D n/spl times/m-grid scroll, and 3-D n/spl times/m/spl times/l-grid scroll chaotic attractors. Two typical cases are investigated in detail: the hysteresis and saturated multiscroll chaotic attractors. A simple blocking circuit diagram is designed for experimentally verifying 1-D 5/spl sim/11-scroll, 2-D 3/spl times/5/spl sim/11-grid scroll, and 3-D 3/spl times/3/spl times/5/spl sim/11-grid scroll hysteresis chaotic attractors by manipulating the switchers. Moreover, a block circuitry is also designed for physically realizing 1-D 10, 12, 14-scroll, 2-D 10, 12, 14/spl times/10-grid scroll, and 3-D 10/spl times/10/spl times/10-grid scroll saturated chaotic attractors via switching. In addition, one can easily realize chaotic attractors with a desired odd number of scrolls by slightly modifying the corresponding voltage saturated function series of the circuit, to produce for instance a 1-D 13-scroll saturated chaotic attractor. This is the first time in the literature to report an experimental verification of a 1-D 14-scroll, a 2-D 14/spl times/10-grid scroll and a 3-D 10/spl times/10/spl times/10-grid (totally 1000) scroll chaotic attractors. Only the 3-D case is reported in detail for simplicity of presentation. It is well known that hardware implementation of 1-D n-scroll with n/spl ges/10, 2-D n/spl times/m-grid scroll with n,m/spl ges/10, and 3-D n/spl times/m/spl times/l-grid scroll with n,m,l/spl ges/10 chaotic attractors is very difficult technically, signifying the novelty and significance of the achievements reported in this paper. Finally, this circuit design approach provides some principles and guidelines for hardware implementation of chaotic attractors with a multidirectional orientation and with a large number of scrolls, useful for future circuitry design and engineering applications.