Chaos Generators

Abstract

Chaos generators can be implemented using discrete electronic devices and more recently using programmable logic like FPGAs. Recent works show that chaotic behavior can be guaranteed by evaluating Lyapunov exponents, and by ensuring that at least one is positive, which is known as maximum Lyapunov exponent (MLE) [20]. Thus, chaos generators presenting high MLE value, high entropy and a good distribution of trajectories in the phase-space portraits, are very much needed to enhance engineering applications. Chaotic oscillators have the challenge on generating multi-scroll attractors with high MLE value, in which their coefficients in the model vary as MLE varies, thus requiring tuning or programming different decimal values. On the one hand, using commercially available discrete electronic devices is not appropriate since they present high sensitivities to circuit element values and the circuitry increases as the number of scrolls does it. On the other hand, discrete active devices cannot tune more than 3 decimals, i.e., due to the high sensitivities of the circuit elements, it is difficult to set coefficient values lower than 0.001. That way, this chapter shows how does an FPGA is useful to observe chaotic attractors generating from 2-scrolls to 50-scrolls.