Adaptive symmetry control in secure communication systems

Chaos-based secure communications is a broadly studied field in nonlinear dynamics. Such technique is traditionally based on chaotic synchronization between master and slave systems implemented as the transmitter and receiver. A common way to encode the message is switching the bifurcation parameters of the master system, which leads to perturbation of the dynamics and often breaks the synchronization. The time of the transient process to restore the identity of the trajectories of the master and slave systems can be unacceptably long for practical applications. Therefore, the development of techniques for fast re-synchronization of models of chaotic systems is of interest. In this paper we propose a novel technique for synchronizing finite-difference models of continuous chaotic systems through adaptive control of the so-called symmetry coefficient. We experimentally confirm that the proposed approach can be faster than the traditional control of the bifurcation parameter. In addition, we discovered that changing the symmetry coefficient in semi-implicit models leads only to a slight deformation of the stability regions of the finite-difference scheme and practically does not affect the nonlinear properties of the simulated chaotic system. The applied analysis shows that detecting a transmitted message through the modulation of the symmetry coefficient is difficult compared to the conventional approach.