Design and Applications of Continuous-Time Chaos Generators

Chaos systems can be classified as one type of complex dynamical systems that possess special features such as being extremely sensitive to tiny variations of initial conditions. In general, for deterministic chaos to exists, a dynamical systemmust have a dense set of periodic orbits, it must be transitive and it has to be sensitive to initial conditions (Strogatz, 2001). Chaos systems have bounded trajectories in the phase space, and they have at least one positive maximum Lyapunov exponent (Dieci, 2002; Lu et al., 2005; Munoz-Pacheco & Tlelo-Cuautle, 2010; Ramasubramanian & Sriram, 2000). Nowadays, several chaos generators have been implemented with electronic devices and circuits in order to have a major impact on many novel applications, as the ones reported in (Cruz-Hernandez et al., 2005; ErgunO Gamez-Guzman et al., 2008; Lin W Strogatz, 2001; Trejo-Guerra et al., 2009). Furthermore, this chapter is mainly devoted to highlight the design automation of continuous-time multi-scroll chaos generators, their implementations by using behavioral models of commercially available electronic devices, their experimental realizations and applications to secure communications. A review of the double-scroll Chua’s circuit is also presented along with the generation of hyperchaos by Coupling Two Chua’s circuits. Basically, we present the generation of multi-scroll attractors by using saturated nonlinear function series. We show their implementation by using traditional operational amplifiers (opamps) and current-feedback operational amplifiers (CFOAs) (Senani & Gupta, 1998). Besides, we summarize some performances of multi-scroll chaos generators by using opamps (Munoz-Pacheco & Tlelo-Cuautle, 2010), CFOAs (Trejo-Guerra, Sanchez-Lopez, Tlelo-Cuautle, Cruz-Hernandez & Munoz-Pacheco, 2010), current conveyors (CCs) (Sanchez-Lopez et al., 2010) and unity-gain cells (UGCs) (Sanchez-Lopez et al., 2008). However, not only the CC and the UGC can be taken from the commercially available CFOA AD844, but also they can be designed with standar integrated complementary metal-oxide-semiconductor (CMOS) technology (Trejo-Guerra, Tlelo-Cuautle, Munoz-Pacheco, Cruz-Hernandez & Sanchez-Lopez, 2010). 10