期刊
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
卷 61, 期 3, 页码 845-853出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2013.2283999
关键词
Bifurcation; fractional-order chaotic system; fractional-order circuits; fractional frequency domain approximation; topological horseshoe theory
资金
- National Natural Science Foundation of China [11202148]
- Natural Science Foundation of China [61174094]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20090031110029]
Based on fractional transfer function approximation in frequency domain, the paper firstly discusses the fractional form of a four-wing autonomous integral-order chaotic system, and finds some chaotic attractors in the different orders of the fractional-order system. The chaotic attractors can be found when the order of the fractional-order system is varied from 1.5 to 2.7, especially in the fractional-order system of the order as low as 2.7, and various chaotic behaviors occur when varying four different system parameters. Some bifurcation diagrams and phase portraits including the four-wing chaotic attractors, the two-wing chaotic attractors, and some periodic orbits are given to verify the chaotic behaviors of the fractional-order system. Then, based on the method of topological horseshoe analysis adopted in many integer-order chaotic systems, a topological horseshoe is found to prove the existence of chaos in the fractional-order system of the order as low as 2.7. At last, an analog circuit is designed to confirm the chaotic dynamics of fractional-order system.
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