Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Abstract

Over the last two decades, theoretical design and circuit implementation of various chaos generators have been a focal subject of increasing interest due to their promising applications in various real-world chaos-based technologies and information systems. In particular, generating complex multiscroll chaotic attractors via simple electronic circuits has seen rapid development. This article offers an overview of the subject on multiscroll chaotic attractors generation, including some fundamental theories, design methodologies, circuit implementations and practical applications. More precisely, the article first describes some effective design methods using piecewise-linear functions, cellular neural networks, nonlinear modulating functions, circuit component design, switching manifolds, multifolded tori formation, and so on. Based on different approaches, computer simulation and circuit implementation of various multiscroll chaotic attractors are then discussed in detail, with some theoretical proofs and laboratory experiments presented for verification and demonstration. It is then followed by some discussion on potential applications of multiscroll chaotic attractors, including secure and digital communications, synchronous prediction, random bit generation, and so on. The article is finally concluded with some future research outlooks, putting the important subject into engineering perspective.

A Brief Overview of Multi-Scroll Chaotic Attractors Generation

“…Similarly,Özoǧuz et al [3] constructed an n−scroll chaotic attractors generator by using the smooth hyperbolic tangent functions, which is described by  ẋ ẏ z…”

“…Multi-scroll chaotic attractors generation has become a relatively mature research direction today, after rapid developments in the last two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

“…Tang et al [7][8] introduced a sine function to generate n−scroll attractors in a simple circuit with physically realizing up to a 10−scroll chaotic attractor observed on the oscilloscope. Similarly,Özoǧuz et al [3] suggested a nonlinear transconductor method for creating n−scroll chaotic attractors. Lü et al [9] presented a switching manifold approach for generating chaotic attractors with multiple-merged basins of attraction.…”

Experimental Confirmation of n—scroll Hyperchaotic Attractors

“…Han et al [7] constructed a double-hysteresis building block to physically realize a 9−scroll chaotic attractor. There are some other approaches reported in the literature for the design and circuit implementation of multi-scroll chaotic attractors [8][9][10][11][12][13][14]. It is generally quite difficult to physically build a nonlinear resistor having an appropriate characteristic with many segments.…”

“…The main obstacle is that the device must have a very wide dynamic range [3,6], however physical conditions always limit or even prohibit such circuit realization [6]. Recently, Lü and Chen [14] reviewed the main advances of multi-scroll chaos generation.…”