Synchronization of Chaotic Systems via Adaptive Control of Symmetry Coefficient in Semi-Implicit Models

In this paper, we introduce the approach for the synchronization of semi-implicit finite-difference schemes using the adaptive symmetry coefficient control. The proposed method is based on the known parametric adaptive control method that is often used in communication schemes for covert data transmission. In such systems, the desired signal is encoded by switching between two values of the nonlinearity parameter of the chaotic system. The vulnerability of this scheme is that the switching can be detected since the properties of the generated signals can differ significantly depending on various values of nonlinearity parameters. In this study, we propose to synchronize semi-implicit schemes using the symmetry coefficient instead of parameters. Thus, synchronized models will generate signals with similar properties and the switching can be less detectable in comparison with the conventional approach. The developed adaptive synchronization technique can be useful in systems for secure data transmitting including secure communication for the industrial Internet of Things.