L.V. Savkin – Lead Designer; Degree Seeker, 

Space Research Institute of RAS, Special Design Bureau of Space Instrumentation (Tarusa);

Kotelnikov Institute of Radioengineering and Electronics of RAS (Moscow) E-mail: solaris.rafo@gmail.com

In this article discusses some features of the decomposition procedure for simplest types of cyclically symmetric dynamical systems (CSDS), which can be used as chaotic oscillators for constructing systems of hidden information transfer with a chaotic carrier. The main attention is paid to the decomposition of nonlinear dynamical systems by representing them in the form of circulant  digraphs to register a synchronous chaotic response. Using three different CSDS with chaotic dynamics as an example, we consider options for implementing solver vertices in the Simulink software package. 

As chaotic dynamical systems are selected:

thomas standard system;

thomas system with cubic nonlinearity; 3) piecewise linear system.

Based on the 5th order Thomas standard system (oscillator), the fact that the break point in the slave CSDS for registering a synchronous chaotic response can be selected between any two adjacent vertices of the digraph is demonstrated. An important requirement is the identity of the parameters of ODE systems that describe the master and slave systems.

The proposed approach is quite convenient to apply when building a CSDS based on FPGA, since most of the modern software packages allow you to generate an HDL-code of the project in the process of numerical simulation. This feature also applies to the Simulink software package, which was involved in this work.

Savkin L.V. Decomposition of cyclically symmetric dynamical systems in the problems of hidden transfer of information using a chaotic carrier. Achievements of modern radioelectronics. 2020. V. 74. № 7. P. 46–54. DOI: 10.18127/j20700784-202007-05. [in Russian]

1. Dmitriev A.S., Panas A.I. Dinamicheskiy khaos: novye nositeli informatsii dlya sistem svyazi. M.: Izd-vo FIZMATLIT. 2002. [in Russian]
2. Pecora L.M., Carrol T.L. Synchronization in chaotic systems. Phys. Rev. Letters. 1990. V. 64. № 8. P. 821–824.
3. Volkovskiy A.R., Rul'kov N.V. Sinkhronnyy khaoticheskiy otklik nelineynoy sistemy peredachi informatsii s khaoticheskoy nesushchey. Pis'ma v ZhTF. 1993. № 3. S. 71–75. [in Russian]
4. Cuomo M.K., Oppenheim A.V., Strogatz S.H. Synchronization of Lorenz-Based Chaotic Circuits with Application to Communications. IEEE Trans. Circuits and Systems. 1993. V. 40. № 10. P. 626.
5. Dedieu H., Kennedy M., Hasler M. Chaos Shift Keying: modulation and demodulation of a chaotic carrier using self-Synchronizing Chua's circuits. IEEE Trans. Circuits and Systems. 1993. V. CAS–40. № 10. P. 634–642.
6. Sprott Dzh. K. Elegantnyy khaos: algebraicheski prostye khaoticheskie potoki. M.-Izhevsk: Institut komp'yuternykh issledovaniy. 2012. [in Russian]
7. Sprott J.C., Chlouverakis K.S. Labyrinth Chaos. International Journal of Bifurcation and Chaos, Appl. Sci. Eng. 2007. V. 17. № 6. P. 2097–2108.