Optimizing the maximum Lyapunov exponent and phase space portraits in multi-scroll chaotic oscillators

This investigation introduces the application of the nondominated sorting genetic algorithm to optimize two characteristics of multiscroll chaotic oscillators: (a) Maximizing the values of the maximum Lyapunov exponent (MLE), and (b) minimizing the dispersions of the phase space portraits (PSP) among all scrolls in an attractor. As shown in this study, these two oscillator's characteristics are in conflict and must be considered at the same time. The cases of study are two multiscroll chaotic oscillators based on piecewise-linear functions, namely: saturated function series and Chua's diode (negative slopes). Basically, a very new procedure to measure the PSP coverture among all generated scrolls is introduced in the optimization loop for each feasible solution maximizing the MLE. The best optimized results are compared with traditional values of the coefficients of the equations describing the oscillators. Finally, we list the values of the optimized MLE and their corresponding PSP when generating from 2- to 6-scroll attractors.