Circuit realization of the synchronization of two chaotic oscillators with optimized maximum lyapunov exponent

Abstract

The modeling, simulation and circuit realization of the synchronization of two optimized multi-scroll chaotic oscillators is described herein. The case of study is the master-slave synchronization of two multi-scroll chaotic oscillators generating four to seven scrolls, based on saturated function series. The maximum Lyapunov exponent (MLE) of the chaotic oscillator is optimized by applying meta-heuristics. We show the behavior on the synchronization for chaotic oscillators with low and high MLEs, while the synchronization is performed by generalized Hamiltonian forms and observer approach from nonlinear control theory. Numerical simulation results are given for the chaotic oscillators with and without optimized MLEs, and for their master-slave synchronization. Finally, we show the good agreement between theoretical results, SPICE simulations and the experimental results when the whole synchronized system is implemented with commercially available operational amplifiers.