Abstract: The most common type of sounding signals of sonar systems are broadband linear-frequency-modulated signals (LFM). Due to the use of such signals it is possible to increase the range and resolving power of hydroacoustic devices, but this does not solve the problem of mutual interference of pulses. One type of broadband signals are chaotic oscillations, which theoretically are able to become an alternative to chirp signals due to increased resistance to crosstalk. The paper compares chaotic and chirp signals by simulating their passage in an aqueous medium. Chaotic signals generated by systems with different numbers of basins of attraction are investigated. The study shows that chaotic signals are more resistant to mutual interference, and also experience less attenuation when propagating in an aqueous medium compared to the types of signals currently used. The stability of chaotic broadband signals to interference and attenuation correlates with the number of basins of attraction of the attractor of the generating chaotic system. Based on the results of the work, it can be concluded that the chaotic signals are used as probing pulses of sonar systems.

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.