Application of Reservoir Computers for Chaos Synchronization and Cracking Chaos-Based Cryptography in Fermionic 2D Thirring and 4D Gursey Models with Spinor Fields

Reservoir computers have recently become one of the most widely exploited model-free approaches to chaos synchronization due to their fast convergence speed and simple yet effective learning rules. In this study, reservoir computing has been utilized to emulate the dynamics of chaotic Thirring and Gursey systems. In the supervised learning of the reservoir, one-step ahead states of the dynamical systems have been employed as the teaching signals. After the training phase, the reservoir was first run autonomously and then weakly driven by chaotic systems. It has been shown that the trained reservoir computers can exhibit the same characteristics as the attractors of the learned chaotic systems, which enable their use in synchronization tasks of chaotic systems with possible application in cracking chaos-based cryptography. To investigate the effect of noise on the performance of reservoir computers, noise signals with different colors and amplitudes have been included in the transmitted signals. The obtained results indicate that the proposed scheme can provide lower error metrics for both models.