Abstract: The article explores the technology of hybrid modeling of chaotic systems in the form of synchronization of digital and analog models of the Rossler system, interacting via analog-digital and digital-analog conversion paths. The unidirectional and bidirectional variants of chaotic synchronization are considered, and the synchronization error is estimated for each of the specified cases. For the analog implementation of the Rössler system, a circuit has been developed based on operational amplifiers, multipliers, and precision passive elements. The digital model of the system is based on a semi-implicit hardware-oriented method of numerical integration of the second order of algebraic accuracy. In order to substantiate the choice of the method, graphs of the performance of various solvers of ordinary differential equations are presented when simulating the Rössler system. It is shown that the chosen semi-implicit numerical integration method has the highest computational efficiency among all second-order methods. Experimentally demonstrated the ability to synchronize analog and digital models of a chaotic system. The synchronization of two and three models of the Rossler system in various variants of the connection topology is considered. By analyzing the synchronization error, it is shown that the greatest accuracy is achieved when using a fully coupled topology, which is based on the bi-directional synchronization method of the three models of the Rössler system.

Abstract: An approach to the selection of a finite-difference scheme of a chaotic pseudo-random sequence generator based on the use of step diagrams (h-diagrams) is proposed. As a test problem, a generator is considered based on the random Rössler system discretized by explicit, implicit and semiquant numerical methods of the first and second order of algebraic accuracy. The sequences generated by different variants of the generator are randomly checked by a battery of NIST statistical tests. Advantages of the proposed approach in the design of chaotic signal generators are shown, consisting in an essential (by an order of magnitude) acceleration of the device design time due to a new method of selecting the discretization step and the discrete operator. The effectiveness of using semi-implicit finite difference schemes in the generation of pseudo-random sequences by the method of numerical solution of chaotic differential equations is confirmed. The obtained results can be used in cryptography applications, in the design of secure communication systems, in solving problems of numerical simulation of dynamical systems and mathematical statistics.