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Abstract and Applied Analysis
Volume 2014, Article ID 495126, 11 pages
Research Article

A Strange Double-Deck Butterfly Chaotic Attractor from a Permanent Magnet Synchronous Motor with Smooth Air Gap: Numerical Analysis and Experimental Observation

1Department of Physics and Electronics Science, Binzhou University, Binzhou 256604, China
2Department of Industry Design, Tianjin University of Science and Technology, Tianjin 300457, China
3Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa
4Department of Automation, Tianjin University of Science and Technology, Tianjin 300457, China
5Department of Automation, Nankai University, Tianjin 300071, China

Received 30 April 2014; Accepted 1 July 2014; Published 17 July 2014

Academic Editor: Roberto Barrio

Copyright © 2014 Zhonglin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A permanent magnet synchronous motor (PMSM) model with smooth air gap and an exogenous periodic input is introduced and analyzed in this paper. With a simple mathematical transformation, a new nonautonomous Lorenz-like system is derived from this PMSM model, and this new three-dimensional system can display the complicated dynamics such as the chaotic attractor and the multiperiodic orbits by adjusting the frequency and amplitude of the exogenous periodic inputs. Moreover, this new system shows a double-deck chaotic attractor that is completely different from the four-wing chaotic attractors on topological structures, although the phase portrait shapes of the new attractor and the four-wing chaotic attractors are similar. The exotic phenomenon has been well demonstrated and investigated by numerical simulations, bifurcation analysis, and electronic circuit implementation.