Synchronization of multi-directional multi-scroll chaos generators: A Hamiltonian approach

In this paper, a chaotic synchronization scheme for multi-directional multi-scroll chaos generators is presented. We use Generalized Hamiltonian forms approach to determine the synchronization conditions for two unidirectionally coupled multi-directional multi-scroll chaotic attractors. First, two state-variables of the master system are used to control the two nonlinear functions in the slave system and consequently, reach the synchronization of two 2D-4-scroll chaotic systems. Similarly, the synchronization of two 3D-4-scroll chaotic systems is achieved by using all three state-variables in order to control the three nonlinear functions for the slave system. Finally, theoretical calculations are in good agreement with numerical simulations and a prediction on the values for observer gain is also given.