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Fractal system as represented by singularity function
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.>
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Citations
Cited by
Chaos and hyperchaos in the fractional-order Rössler equations
Li, C., & Chen, G. (2004) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/j.physa.2004.04.113 · Cited by 685
Chaos in the fractional order Chen system and its control
Li, C., & Chen, G. (2004) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2004.02.035 · Cited by 573
Synchronization of chaotic fractional-order systems via active sliding mode controller
Tavazoei, M. S., & Haeri, M. (2008) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.08.039 · Cited by 260
He, C., Chen, Z., Wang, L., Wu, X., Liu, T., & Long, B. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad3409 · Cited by 11
Metadata
- Authors
- Charef, A., Sun, H. H., Tsao, Y. Y., & Onaral, B.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1992
- Volume
- 37
- Issue
- 9
- Pages
- 1465-1470
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2155572235
- Cited by
- 673
- References
- 0
- FWCI
- 2.58
- Type
- journal article
- Language
- en
- Open access
- closed
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