Hyperchaotic N-Scroll Attractors

Yalçın, Mehmet Ali; Suykens, Johan A. K.; Vandewalle, Joos

doi:10.1142/9789812792662_0005

Cited by 16 publications

(8 citation statements)

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“…To generate n-double scroll hyperchaotic attractors from (55), Yalcin et al [2000a] modified the PWL characteristic (56) as follows:…”

Section: Hyperchaotic Multiscroll Attractors From the Modified Mck CImentioning

confidence: 99%

“…Aziz-Alaoui [1999 then presented a PWL function approach for creating multispiral chaotic attractors from both autonomous and nonautonomous differential equations. Yalcin et al [2000a] introduced a technique for generating a family of n-double-scroll hyperchaotic attractors. Yalcin et al [2001] also proposed a simple circuit model for generating n-scroll chaotic attractors.…”

Section: Introductionmentioning

confidence: 99%

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Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Lü

Chen

2006

Int. J. Bifurcation Chaos

496

181

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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.

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“…To generate n-double scroll hyperchaotic attractors from (55), Yalcin et al [2000a] modified the PWL characteristic (56) as follows:…”

Section: Hyperchaotic Multiscroll Attractors From the Modified Mck CImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Lü

Chen

2006

Int. J. Bifurcation Chaos

496

181

View full text Add to dashboard Cite

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“…Alaoui et al presented multispiral chaotic attractors using PWL function approach for both autonomous and non-autonomous differential equations [8,9]. Yalcin et al introduced a hyperchaotic attractor technique for generating a family of multi-scroll, and they also proposed a simple circuit model for generating multi-scroll chaotic attractors [10,11]. Lü et al proposed multi-scroll chaotic attractors using hysteresis series method, saturated function series approach and thresholding approach [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Multi-Scroll Chaotic Attractors in SC-CNN via Hyperbolic Tangent Function

Günay

Altun

2018

Electronics

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A State Controlled-Cellular Neural Network (SC-CNN) based chaotic model for generating multi-scroll attractors via hyperbolic tangent function series is proposed in this paper. After presenting the double scroll generation, the presented SC-CNN system is used in multi-scroll chaotic attractor generation by adding hyperbolic tangent function series. By using equilibrium analysis and their stability such as Lyapunov exponent analysis, bifurcation diagrams and Poincaré map, the dynamical behaviors of the proposed system are theoretically analyzed and numerically investigated.

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“…For an autonomous hyperchaotic system, suppose that its trajectories are globally bounded. In this case, it is easy to place the zero and negative Lyapunov exponents into the underlying system [21][22][23][24], but the key step actually is how to place the positive Lyapunov exponents as required [25][26][27][28][29]. This problem has not been completely solved to date.…”

Section: Introductionmentioning

confidence: 99%

Constructing hyperchaotic systems at will

Shen

Lü

et al. 2015

Circuit Theory & Apps

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Summary Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher‐dimensional dissipative hyperchaotic systems by using a single‐parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed‐loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle‐focus equilibria. For the non‐degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10‐dimensional hyperchaotic systems, and the experimental observation is also given. Copyright © 2015 John Wiley & Sons, Ltd.

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Hyperchaotic N-Scroll Attractors

Cited by 16 publications

References 0 publications

Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Multi-Scroll Chaotic Attractors in SC-CNN via Hyperbolic Tangent Function

Constructing hyperchaotic systems at will

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