A New Look at Chua's Circuit

Over the past two decades, researchers have been greatly interested in nonlinear dynamical systems with a special attention to those having chaotic behavior. This is due to the appearance of chaos in many scientific disciplines such as biology, chemistry, physics, mathematics and engineering applications [Skinner, 1994; Arneodo et al., 1993; Wolframm, 1985; Zhusubaliyev & Mosekilde, 2003; Lankalapalli & Ghosal, 1997]. Hence, a myriad of papers have been published to present the peculiarity of chaotic dynamics. To this regard, the emergence of new mathematical and numerical tools played a crucial role to understand, characterize and quantify chaos. Actually, the research on chaotic systems can be classified into three main streams: investigating new chaotic systems, synchronizing chaotic systems and controlling chaos. Our present paper falls within the first stream. In early sixties of the last century, E. N. Lorenz has confirmed that the chaotic behavior was not artifacts of numerical simulations but was inherent in the model of thermally induced fluid convection in the atmosphere [Lorenz, 1963]. Since then, several other systems have been coined and shown to exhibit chaos. Chua’s system [Chua, 2010] is one that has served as a workhorse for chaos characterization and analysis as well as for testing the elaborated synchronization and control methods. Chua’s circuit is a paradigm for chaos which is considered as the simplest nonlinear electrical circuit that exhibits almost known chaotic phenomenon [Madan, 1993]. Many attempts to modify Chua’s circuit are reported in literature. Most of them are concerned with the modification of the nonlinear element characteristics [Zhong, 1994; Yalcin et al., 2001; Tang et al., 2001; Thamilmaran et al., 2004] or deal with increasing the dimension of Chua’s circuit [Yuan-Zhao, 1996]. Few others have offered serious suggestions to substitute the inductor element with the purpose to implement Chua’s circuit on an integrated circuit [Morgül, 1995a, 1995b; Tôrres & Aguirre, 2000; Tadayon et al., 2008]. To our knowledge, very few works have presented explanations on how to choose the circuit