On the relation between the synchronization error and the number of synchronized state-variables in 3D chaos generators

In this paper, a study of the effects on using a different number of control signals in the synchronization of multi-directional multi-scroll chaos generators is presented. We adopt Generalized Hamiltonian forms approach to synchronize two 3D multi-scroll chaotic attractors. First, it is used only one state-variable (x, y, z) from the master system in order to control only one nonlinear function in the slave system. Alike, there are used two (x-y, y-z, x-z) or three (x-y-z) state-variables to attain the synchronization between the master and slave systems by means of controlling two or three nonlinear functions. Finally, numerical simulations results support the study by shown the synchronization error for the possible permutations and a prediction of the performance is summarized.