Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2013, Article ID 875965, 8 pages http://dx.doi.org/10.1155/2013/875965 Research Article Chaotic Motions in the Real Fuzzy Electronic Circuits Shih-Yu Li, 1,2 Cheng-Hsiung Yang, 3 Chin-Teng Lin, 2,4 Li-Wei Ko, 1,2 and Tien-Ting Chiu 5 1 Department of Biological Science and Technology, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan 2 Brain Research Center, National Chiao Tung University, Hsinchu, Taiwan 3 Department of Automatic Control, National Taiwan University of Science and Technology, Taipei City, Taiwan 4 Institute of Electrical Control Engineering, National Chiao Tung University, Hsinchu, Taiwan 5 Department of Industrial and Systems Engineering, Chung Yuan Christian University, Chung-Li, Taiwan Correspondence should be addressed to Shih-Yu Li; agenghost@gmail.com Received 26 October 2012; Accepted 30 December 2012 Academic Editor: Chuandong Li Copyright © 2013 Shih-Yu Li et al. is 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. Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions, and unpredictability. Consequently, generating chaotic signals on electronic circuit to produce real electrical signals applied to secure communications is an exceedingly important issue. However, nonlinear systems are always composed of many complex equations and are hard to realize on electronic circuits. Takagi-Sugeno (T-S) fuzzy model is a powerful tool, which is described by fuzzy IF-THEN rules to express the local dynamics of each fuzzy rule by a linear system model. Accordingly, in this paper, we produce the chaotic signals via electronic circuits through T-S fuzzy model and the numerical simulation results provided by MATLAB are also proposed for comparison. T-S fuzzy chaotic Lorenz and Chen-Lee systems are used for examples and are given to demonstrate the effectiveness of the proposed electronic circuit. 1. Introduction Nonlinear dynamics, commonly called the chaos theory, changes the scientific way of looking at the dynamics of natural and social systems, which has been intensively studied over the past several decades [1–10]. e phenomenon of chaos has attracted widespread attention amongst mathema- ticians, physicists, and engineers and has also been exten- sively studied in many fields, such as chemical reactions [11, 12], biological systems [13, 14], information processing [15, 16], and secure communications [17–20]. e mathematical meteorologist Lorenz discovered chaos in a simple system of three autonomous ordinary differential equations in order to describe the simplified Rayleigh-B´ enard problem [21] in 1963 which is the most popular system for studying [22–26]. Chen and Lee reported a new chaotic system [27] in 2004, which is now called the Chen-Lee system [28]. e chaotic Chen-Lee system was developed based on the Euler equations for the motion of rigid body. It was proved that this system is the governing set of equations for gyromo- tion with feedback control. Recently, studies were conducted on this system to explore its dynamic behavior, including the fractional order behavior, the generation of hyperchaos and perturbation analysis, the control and anti-control of chaos, and the synchronization [29, 30]. Since the fuzzy set theory [31] and the fuzzy logic [32] were initiated by Zadeh in 1965 and 1973, fuzzy logic has received much attention as a powerful tool for the nonlinear filed. Among various kinds of fuzzy methods, Takagi-Sugeno fuzzy system is widely accepted as a tool for design and analy- sis of fuzzy control system [33]. e T-S fuzzy model proposes a successful method to deal with certain complex nonlinear systems via some local linear subsystems. ere are plenty of researches using the Takagi-Sugeno (T-S) fuzzy model to represent typical chaotic models and then apply some effec- tive fuzzy techniques [34–42]. However, there are still no real