Design and Analysis of Multiscroll Chaotic Attractors From Saturated Function Series

Lü, Jinhu; Chen, Guanrong; Yu, Xinghuo; Leung, Henry

doi:10.1109/tcsi.2004.838151

Cited by 297 publications

(63 citation statements)

References 22 publications

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“…where x, y and z are the state variables; a, b, c and d 1 are constant coefficients and f (x) is a nonlinear function that can be approximated by a piecewise-linear (PWL) one to describe the well-known chaotic oscillator based on saturated function series [13]. The PWL function can be increased systematically, as already shown in [8], where the number of saturated segments equals the number of scrolls to be generated.…”

Section: Double-scroll Chaotic Oscillatormentioning

confidence: 99%

Application of a Chaotic Oscillator in an Autonomous Mobile Robot

Tlelo‐Cuautle

Ramos-López

Sanchez-Sanchez

et al. 2014

Journal of Electrical Engineering

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Terrain exploration robots can be of great usefulness in critical navigation circumstances. However, the challenge is how to guarantee a control for covering a full terrain area. That way, the application of a chaotic oscillator to control the wheels of an autonomous mobile robot, is introduced herein. Basically, we describe the realization of a random number generator (RNG) based on a double-scroll chaotic oscillator, which is used to guide the robot to cover a full terrain area. The resolution of the terrain exploration area is determined by both the number of bits provided by the RNG and the characteristics of step motors. Finally, the experimental results highlight the covered area by painting the trajectories that the robot explores.

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Section: Double-scroll Chaotic Oscillatormentioning

confidence: 99%

Application of a Chaotic Oscillator in an Autonomous Mobile Robot

Tlelo‐Cuautle

Ramos-López

Sanchez-Sanchez

et al. 2014

Journal of Electrical Engineering

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“…Therefore, the generation of MSCA is a subject of increasing interest, and a considerable number of researchers have done work in this field. [4][5][6][7][8][9][10][11][12][13] For example, Tang et al introduced a sine-function approach to generate n-scroll attractors, and a 9-scroll-attractor was observed for the first time. 4,5 Later, Yalcin et al presented a family of multi-directional, MSCA by adopting a stair nonlinear function series (SNFS) method, including 1-D n-scroll, 2-D n Â m-scroll, and 3-D n Â m Â p-scroll attractors.…”

Section: Introductionmentioning

confidence: 99%

“…[7][8][9][10][11] Soon afterwards, L€ u et al proposed a saturated nonlinear function (SNLF) approach to create 1-D, 2-D, and 3-D multi-directional MSCA. 12 Zhang and Yu introduced two different kinds of piecewise-linear functions (PWLF) to generate multi-directional MSCA in a single system. 13 Nowadays, there are many methods to design and realize MSCA in the classical differential systems.…”

Section: Introductionmentioning

confidence: 99%

Design and implementation of grid multi-scroll fractional-order chaotic attractors

Chen

Pan

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper proposes a novel approach for generating multi-scroll chaotic attractors in multidirections for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincar e section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 Â 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.With the development of fractional-order (FO) calculus, it is well verified that many nonlinear FO differential systems, such as the FO Duffing oscillator, the FO Chua circuit, or the so-called FO R€ ossler, FO Chen, FO Lorenz, and FO L€ u systems, among others, exhibit complex bifurcations and chaotic phenomena. These systems can generate single-scroll or double-scroll chaotic attractors. Multi-scroll chaotic attractors (MSCA) admit much more complex dynamic behaviors, more adjustability, and more encryption parameters. Therefore, MSCA have more potential application to communications, cryptography, and many other fields. Naturally, the design and implementation of fractional MSCA is an interesting and challenging topic. In this paper, a new MSCA generation method will be introduced, which is different from the existing ones. In addition, circuit experimental results of the generation of fractional MSCA are presented.

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“…Much research has been devoted to searching for new chaotic systems of autonomous ordinary differential equations (ODEs) with particular desired dynamic properties. With improvements in circuit realization technology through the development of integrated circuits, multi-scroll [1,2,3] and multi-wing chaotic systems have aroused special interest, especially four-wing attractors [4,5,6,7,8] and grid multi-wing chaotic systems [9,10,11]. It is known that wing attractors from a chaotic system generally arise from some symmetry, and when that symmetry is broken, the chaotic flow may drop into a different petal of the wing.…”

Section: Introductionmentioning

confidence: 99%

A novel four-wing strange attractor born in bistability

Pehlivan

Sprott

et al. 2015

IEICE Electron. Express

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Attractor merging can exist in chaotic systems with some kind of symmetry, which makes it possible to form a four-wing attractor from a bistable system. A relatively simple such case is described, which has robust chaos varying from a pair of coexisting symmetric single-wing attractors to a double-wing butterfly attractor, and finally to a four-wing attractor. Basic dynamical characteristics of the system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, and Poincaré sections. From a broad exploration of the dynamical regions, we observe robust chaos with embedded Arnold tongues of periodicity in selected parameter regions. The chaotic system with a wing structure has four nonlinear quadratic terms, one of the coefficients of which is a hidden isolated amplitude parameter, by which one can control the amplitude of two of the variables. The corresponding chaotic circuit with an amplitude-control knob is designed and implemented, which generates a four-wing attractor with adjustable amplitude.

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Design and Analysis of Multiscroll Chaotic Attractors From Saturated Function Series

Cited by 297 publications

References 22 publications

Application of a Chaotic Oscillator in an Autonomous Mobile Robot

Application of a Chaotic Oscillator in an Autonomous Mobile Robot

Design and implementation of grid multi-scroll fractional-order chaotic attractors

A novel four-wing strange attractor born in bistability

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