Generating Multi-Scroll Chaotic Attractors via Switched Fractional Systems

Sun, Guanghui; Wang, Mao; Huang, Ling; Shen, Liqun

doi:10.1007/s00034-011-9272-2

Cited by 27 publications

(13 citation statements)

References 23 publications

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“…It should be noted that most of the aforementioned MSCA were only verified by numerical simulations. [31][32][33][35][36][37] Here, circuit experiments have been carried out, which coincide with the theoretical results.…”

supporting

confidence: 69%

“…Moreover, it should be pointed out that these aforementioned MSCA, created from FO systems, were only verified by numerical simulations. [31][32][33][35][36][37] To the best of our knowledge, there are few results about circuit realization of MSCA generated from FO systems. Nonetheless, it is more substantive to implement the FO system by circuits than merely by simulating them.…”

Section: Introductionmentioning

confidence: 99%

“…[31][32][33] Sun et al discussed the generation of MSCA based on the switched FO multi-model systems. 35 Ahmad 36 demonstrated that multiple-scroll attractors can be obtained from FO chaotic systems by using a modified nonlinearity and an appropriate set of control parameters. Xu 37 investigated the generation of multi-wing chaotic attractors using integer and FO linear differential equation systems with switching controls.…”

Section: Introductionmentioning

confidence: 99%

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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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supporting

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…As the first strategy, the controller is applied when system is chaotic or in the other words the largest Lyapunov exponent is positive. Lyapunov exponents give a measure of sensitivity of the nonlinear system to control input and initial condition [11,17,20]. When the largest Lyapunov exponent is positive, we can control the chaotic system by rather smaller control inputs.…”

Section: Proposed Adaptive Fuzzy Controller Design Methodologymentioning

confidence: 99%

Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method

Ayati

2011

Circuits Syst Signal Process

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This paper presents an adaptive fuzzy controller for Nonlinear in Parameters (NLP) chaotic systems with parametric uncertainties. In the proposed controller, the unknown parameters are estimated by the novel Improved Speed Gradient (ISG) method, which is a modification of Speed Gradient (SG) algorithm. ISG employs the Lagrangian of two suitable objective functionals for on-line estimation of system parameters. The most significant advantage of ISG is that it is applicable to NLP systems and it results in a faster rate of convergence for the estimated parameters than the SG method. Estimated parameters are used to design the fuzzy controller and to calculate the Lyapunov exponents of the chaotic system adaptively. Furthermore, established on the well-known Takagi-Sugeno (T-S) fuzzy model, a LMI (Linear Matrix Inequality)-based fuzzy controller is designed and is tuned using estimated parameters and Lyapunov exponents. Throughout the controller design procedure, several important issues in fuzzy control theory including relaxed stability analysis, control input performance specifications, and optimality are taken into account. Combination of ISG parameter estimation method and T-S-based fuzzy controller yields an adaptive fuzzy controller capable to suppress uncertainties in parameters and initial states of NLP chaotic systems. Finally, simulation results are provided to show the effectiveness of the ISG and adaptive fuzzy controller on chaotic Lorenz system and Duffing oscillator.

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“…During the last decade, theoretical design and circuit implementation of various multiscroll chaos generators have been a focal subject of increasing interest in electronics engineering (Gandhi & Roska, 2009;Lü & Chen, 2006;Lü, Chen, Yu, & Leung, 2004;Sun, Wang, Huang, & Shen, 2011;Trejo-Guerra, Tlelo-Cuautle, Carbajal-Gomez, & Rodriguez-Gomez, 2013; Trejo-Guerra, Tlelo-Cuautle, Jiménez-Fuentes, Trejo-Guerra et al, 2012;Yalcin, Suykens, & Vandewalle, 2000). For instance, a multi-scroll chaotic oscillator based on saturated nonlinear function (SNLF) series is well described by Lü et al (2004).…”

Section: Introductionmentioning

confidence: 96%

Frequency limitations in generating multi-scroll chaotic attractors using CFOAs

Muñoz‐Pacheco

Tlelo‐Cuautle

Toxqui-Toxqui

et al. 2014

International Journal of Electronics

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The current-feedback operational amplifier (CFOA) allows us to implement any kind of circuit useful in analogue signal processing applications. However, it has limited performance in implementing nonlinear circuits. That way, this investigation highlights the experimental results of implementing a multi-scroll chaotic oscillator by using the commercially available CFOA AD844. The chaotic oscillator is based on saturated nonlinear function (SNLF) series, and we show and discuss its frequency limitations to generate 3-to 10-scrolls from 1 kHz to 100 kHz. Finally, we conclude that the frequency limitations are due to the nonideal characteristics of the CFOA-based SNLF block, imposed by the AD844.

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Generating Multi-Scroll Chaotic Attractors via Switched Fractional Systems

Cited by 27 publications

References 23 publications

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

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

Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method

Frequency limitations in generating multi-scroll chaotic attractors using CFOAs

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