ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ponomarenko V. P. Peculiarities of complex dynamics and transitions to chaotic regimes in the model of two interacting systems with phase control. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 5, pp. 73-93. DOI: 10.18500/0869-6632-2006-14-5-73-93

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2006no5p073.pdf
(downloads: 165)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
621.391.01
DOI: 
10.18500/0869-6632-2006-14-5-73-93

Peculiarities of complex dynamics and transitions to chaotic regimes in the model of two interacting systems with phase control

Autors: 
Ponomarenko Valerij Pavlovich, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Abstract: 

The work is devoted to investigation of complex dynamics in the model of two interacting systems with phase and delay control. Stability conditions of synchronous regime are determined. The processes of excitement of nonsynchronous regimes and transitions between them are considered. Scenarios of development of nonsynchronous regimes under variation of the systems parameters are determined. Routes to chaotic behavior of the model are discussed. Results are presented in the form of one-parameter bifurcation diagrams and phase portraits of the model attractors.

Key words: 
-
Reference: 
  1. Ponomarenko VP, Matrosov VV. Dynamic modes and bifurcations during interaction of two synchronization systems through mutual cross-links. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(6):51.
  2. Ponomarenko VP, Matrosov VV. Excitation of chaotic oscillations in the model of two connected systems with phase control. Journal of Communications Technology and Electronics. 2000;45(8):984–992.
  3. Babich OA. Information processing in radio navigation systems. Moscow: Mashinostroenie; 1991. 511 p. (In Russian).
  4. Tuzov GI, Sivov VA, Prytkov VI. et al. Noise immunity of radio systems with complex signals. Ed. GI. Tuzova. Moscow: Radio i svyaz; 1985. 264 p. (In Russian).
  5. Volynkin AI, Kudryavtsev IV, Mishchenko IN, Shebshaevich VS. Consumer equipment of SRNS "Navstar". Telecommunications and Radio Engineering. 1983;4:70–91.
  6. Chastikov AV, Petrov EP, Prozorov DE. A Filtering Method for Noiselike Signals Formed on the Basis of Recurrent Pseudorandom Sequences of Maximum Period. Journal of Communications Technology and Electronics. 2001;46(5):512–516.
  7. Belyaev RV, Kalinin VI, Kolesov VV. Formation of a noise-like carrier in spectrum expansion communication systems. Communications Technology and Electronics. 2001;46(2):214–223.
  8. Petrov EP, Prozorov DE. Synthesis of devices for the fast search for noiselike signals that are based on multidigit recurrent sequences of the maximum period. Communications Technology and Electronics. 2005;50(10):1281–1286.
  9. Shalfeev VD, Matrosov VV. Chaotically modulated oscillations in related phase systems. In book: Nonlinear Waves 2002. Ed. AV. Gaponov-Grekhov, VI. Nekorkin. Nizhny Novgorod: IPF RAS; 2003. P.77. (In Russian).
  10. Shakhtarin BI, Sidorkina YuA, Aliver VYu, Kobylkina PI. Investigations Of Operating Modes Of Chaos Oscillators. Communications Technology and Electronics. 2003;48(12):1471–1483.
  11. Dmitriev AS, Shirokov ME. Choice of generator for a direct chaotic communications system. Communications Technology and Electronics. 2004;49(7):840–849.
  12. Ponomarenko VP. Dynamic properties of the system for synchronizing a complex signal with additional communication via control circuits. Soviet Journal of Communications Technology and Electronics. 1985;30(3):534.
  13. Shakhgildyan VV, Lyakhovkin AA. Phase-locked frequency adjustment systems. Moscow: Svyaz; 1972. 224 p. (In Russian).
  14. Belyustina LN, Belykh VN. Qualitative investigation of a dynamical system on a cylinder. Differ. Uravn. 1973;9(3):403–415.
  15. Ponomarenko VP, Matrosov VV. Automation of studies of non-linear dynamics of synchronization systems. Bulletin of the Verkhne-Volga branch of the ATN of the RF. High technology in electronics. N. Novgorod. 1997;2(4):15. (In Russian).
  16. Matrosov VV. Dynamics of nonlinear systems. A software package for the study of nonlinear dynamical systems with continuous time. Educational and methodological development. N. Novgorod: Publishing House of UNN; 2002. 54 p. (In Russian).
  17. Neymark YuI, Landa PS. Stochastic and chaotic fluctuations. Moscow: Nauka; 1987. 422 p. (In Russian).
  18. Berge P, Pomeau Y, Vidal C. L’Ordre Dans Le Chaos. Paris: Hermann; 1988. 353 p.
Received: 
12.04.2006
Accepted: 
12.04.2006
Published: 
30.11.2006
Short text (in English):
PDF icon a2006no5p073.doc_.pdf
(downloads: 85)
  • 1565 reads