Journal ArticleDOI
Fractal system as represented by singularity function
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In this article, a singularity function method is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section, which can be simulated by a combination of singularity functions, each representing a single-fractal system.Abstract:
A fractional slope on the log log Bode plot has been observed in characterizing a certain type of physical phenomenon and has been called the fractal system or the fractional power pole. In order to represent and study its dynamical behavior, a singularity function method is presented which consists of cascaded branches of a number of pole-zero (negative real) pairs or simple RC section. The distribution spectrum of the system can also be easily calculated, and its accuracy depends on a prescribed error specified in the beginning. The method is then extended to a multiple-fractal system which consists of a number of fractional power poles. The result can be simulated by a combination of singularity functions, each representing a single-fractal system. >read more
Citations
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Journal ArticleDOI
Chaos in a fractional order Chua's system
TL;DR: In this article, the effects of fractional dynamics in chaotic systems were studied and it was demonstrated that systems of "order" less than three can exhibit chaos as well as other nonlinear behavior.
Proceedings ArticleDOI
Fractional order control - A tutorial
TL;DR: A tutorial on fractional calculus in controls is offered which may make fractional order controllers ubiquitous in industry and several typical known fractional orders controllers are introduced and commented.
Journal ArticleDOI
Chaos and hyperchaos in the fractional-order Rössler equations
Chunguang Li,Guanrong Chen +1 more
TL;DR: In this paper, the authors numerically studied the chaotic behaviors in the fractional-order Rossler equations and found that chaos and hyperchaos exist in such systems with order less than 3.
Journal ArticleDOI
Chaos in the fractional order Chen system and its control
Chunguang Li,Guanrong Chen +1 more
TL;DR: In this paper, the authors studied the chaotic behaviors in the fractional order Chen system and found that chaos exists in all the levels of the Chen system with order less than 3.1.
Journal ArticleDOI
Chaos in Chen's system with a fractional order
Changpin Li,Guojun Peng +1 more
TL;DR: In this paper, the authors used fractional calculus techniques to construct phase diagrams in Chen's system with fractional order and found that chaos does exist in the system with a fractional ordering, and some phase diagrams are constructed.
References
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Journal ArticleDOI
Low-frequency fluctuations in solids: 1/f noise
Pulak Dutta,P. M. Horn +1 more
TL;DR: In this article, the authors deal with selected topics regarding the properties of simple condensed matter systems, especially metals, and find that considerable experimental and conceptual progress has been made, but specific physical processes mostly remain to be identified.
Journal ArticleDOI
Linear approximation of transfer function with a pole of fractional power
TL;DR: In this paper, two methods for the linear approximation of a transfer function with a pole of fractional power are presented, and the Pade method gives a better approximation than Wang and Hsia's method within the frequency limit as specified.
Journal ArticleDOI
Fractal model for the ac response of a rough interface
TL;DR: A fractal model is proposed for a rough interface between two materials of very different conductivities, e.g., an electrode and an electrolyte, which provides insight into the conducting properties of the percolating cluster and the source of the 1/f noise in electronic components.
Journal ArticleDOI
Some noises with I/f spectrum, a bridge between direct current and white noise
TL;DR: The present paper reinterprets spectral measurements without paradox, by introducing a concept to be called "conditional spectrum," and examples are given of functions ruled by chance, that have the observed "erratic" behavior and conditional spectral density.