Complete chaos synchronization of two identical Lorenz systems using nonlinear active control.

Complete synchronization scheme was explored in this work. In this approach we make use of thenonlinear active controller to ensure the synchronization between the master and slave systems, withidentical parameters and initial conditions, to ensure reliable and stable state of the synchronization. Theapproach demonstrates a robust process, as the active controller being designed ensures the two identicalsystems synchronize over time. Tested against mismatched initial conditions we were able to verify thesensitivity of the Lorenz system towards initial conditions, the phase portrait and butterfly effect of thesystem was also illustrated to affirm the validity of this claim, the method demonstrate resilience towardsmismatching initial conditions, giving room to areas of possible application such as securingcommunication, signal processing and control theory.