Title :
Chaotic Characteristics Analysis and Circuit Implementation for a Fractional-Order System
Author :
Jia, H.Y. ; Chen, Zhi Qiao ; Qi, G.Y.
Author_Institution :
Dept. of Autom., Tianjin Univ. of Sci. & Technol., Tianjin, China
Abstract :
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.
Keywords :
analogue circuits; bifurcation; chaos; frequency-domain analysis; transfer functions; analog circuit; bifurcation diagrams; chaotic attractors; chaotic behaviors; chaotic characteristics analysis; chaotic dynamics; circuit implementation; four-wing autonomous integral order chaotic system; fractional order system; fractional transfer function approximation; frequency domain; many integer order chaotic system; topological horseshoe analysis; Analog circuits; Approximation methods; Bifurcation; Chaos; Frequency-domain analysis; Numerical simulation; Orbits; Bifurcation; fractional frequency domain approximation; fractional-order chaotic system; fractional-order circuits; topological horseshoe theory;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2013.2283999