On the synchronization of 1D and 2D multi-scroll chaotic oscillators

Abstract

In this chapter, the guidelines to synchronize one-directional (1D) and two-directional (2D) multi-scroll chaos generators by means of Generalized Hamiltonian forms are presented. First, the multi-scroll chaotic oscillator is simulated at the electronic system level by applying state-variables and piecewise-linear approaches. Besides, we apply scaling procedures to modify the breaking points, slopes and frequency of the chaotic signals in order to reduce their excursion levels within practical values for electronic devices. Second, a chaotic synchronization scheme for multi-directional multi-scroll chaos generators is introduced. We use Generalized Hamiltonian forms approach to determine the synchronization conditions when one and two state-variables of the master system are sent to control the nonlinear functions in the slave system. Additionally, two schemes are set-up to transmit encrypted binary and analog signals by applying chaotic switching technique and additive chaotic masking, respectively. Both schemes are implemented by using traditional operational amplifiers. Finally, theoretical results are confirmed by performing numerical and SPICE simulation results. © Springer-Verlag Berlin Heidelberg 2013.