Chaotifying Fuzzy Hyperbolic Model Using impulsive and Nonlinear Feedback Control Approaches

In the past decade, there have been some studies about control methods with the purpose of either reducing “bad” chaos or introducing “good” chaos [Chen & Dong, 1998]. Due to its great potential in nontraditional applications such as those found within the context of physical, chemical, mechanical, electrical, optical, and particularly, biological and medical systems [Chen et al., 2001; Schiff et al., 1994; Yang et al., 1995], making a nonchaotic system chaotic or maintaining existing chaos, known as “chaotification” or “anticontrol”, has attracted increasing attention in recent years. The process of chaos control is now understood as a transition from chaos to order and sometimes from order to chaos, depending on the purposes of different applications. Studies have shown that discrete maps can be chaotified in the sense of Devaney or Li–Yorke by a state-feedback controller with a uniformly bounded control-gain sequence designed to make all Lyapunov exponents of the controlled system strictly positive or arbitrarily assigned [Chen & Lai, 1997; Chen & Lai, 1998; Wang & Chen, 1999; Wang & Chen, 2000a, 2000b, 2000c]. Even though there is some research work indicating that a kind of continuous stable systems can be chaotified [Lü et al., 2002; Sanchez et al., 2001; Tang et al., 2001; Wang et al., 2000; Wang et al., 2001; Yang et al., 2002; Zhong et al., 2001], it is still an open problem on