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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 209718, 11 pages
http://dx.doi.org/10.1155/2013/209718
Research Article

Chaos Analysis and Synchronization Control of Coronary Artery Systems

1Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, Taichung 41170, Taiwan
2Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan

Received 15 September 2013; Accepted 27 September 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Cheng-Chi Wang and Her-Terng Yau. 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.

Abstract

The present study uses the differential transformation method to solve the governing equations of the coronary artery system and then analyzes the dynamic behavior of the system by means of phase portraits, power spectra, bifurcation diagrams, and Poincaré maps. Also, a master-slave control system is proposed to suppress the nonlinear chaotic behavior of the coronary artery system. The results show that the dynamic behavior of the coronary artery system is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the motion changes from -periodic to 2 -periodic, then from 4 -periodic to 8 -periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0.3 to 0.6 and from 4.5 to 5.9. In addition, it is shown that the proposed control scheme enables the coronary artery system to be synchronized to any state asymptotically such that the risk of cardiopathy is reduced.