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

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Ponomarenko V. P. Dynamical processes in coupled system with phase control. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 1, pp. 47-62. DOI: 10.18500/0869-6632-2003-11-1-47-62

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.391.01
DOI: 
10.18500/0869-6632-2003-11-1-47-62

Dynamical processes in coupled system with phase control

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

Properties of collective behaviour of two coupled phase-locked аnd delay-locked systems are investigated. One of the systems demonstrates simple regular dynamics while the other system exhibits both regular and chaotic regimes. The bifurcation diagram is determined, the regions with the state of phase synchronization, periodic and chaotic nonsynchronous regimes of interacting systems are found. Scenarios of development of nonsynchronous regimes under variation of the system parameters are established. The possibilities оf control over properties аnd regions оf existence оf dynamical regimes are ascertained by changing оf system’s parameter values.

Key words: 
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Acknowledgments: 
This work was supported by the Scientific Programme "Universities of Russia" (project UR.03.01.027) and RFBR (project No. 02-02-17573).
Reference: 
  1. Ponomarenko VP. Dynamics of a nonlinear two-loop tracking system with unidirectional connections. Izvestia RAS. Theory and Control Systems. 1999;(1):115–124 (in Russian).
  2. Ponomarenko VP, Kuzovkin SA. Oscillations in a two-ring system of coupled controlled generators. Izvestiya VUZ. Applied Nonlinear Dynamics. 1998;6(5):28–40 (in Russian).
  3. Tuzov GI, Sivov VA, Prytkov VI. Noise Immunity of Radio Systems with Complex Signals. Moscow: Radio I Svyaz’; 1985. 264 p. (in Russian).
  4. Belykh VN, Nekorkin VI. Qualitative structures and bifurcations generated by a nonlinear third-order phase synchronization equation. Journal of Applied Mathematics and Mechanics. 1978;42(5):871–884. DOI: 10.1016/0021-8928(78)90034-5.
  5. Belyustina LN, Kiveleva KG, Fraiman LA. Qualitative-numerical method in the study of three-dimensional nonlinear SPS. In: Shakhgildyan VV, Belyustina LN, editors. Phase Synchronization Systems. Ch. 2. Moscow: Radio I Svyaz’; 1982. P. 21–45 (in Russian).
  6. Matrosov VV. Regular and chaotic oscillations of the phase system. Tech. Phys. Lett. 1996;22(23):4–8 (in Russian).
  7. Ponomarenko VP, Matrosov VV. Automation of studies of nonlinear dynamics of synchronization systems. Bulletin of the Upper Volga Branch of the ATS of the Russian Federation. High Technologies in Radio Electronics. 1997;2(4):15–21 (in Russian).
  8. Neimark YI, Landa PS. Stochastic and Chaotic Oscillations. Moscow: Nauka; 1987. 424 p. (in Russian).
  9. Anishchenko VS. Complex Oscillations in Simple Systems. Moscow: Nauka; 1990. 312 p. (in Russian).
  10. Shilnikov LP. A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type. Mathematics of the USSR-Sbornik. 1970;10(1):91–102. DOI: 10.1070/SM1970v010n01ABEH001588.
  11. Belyakov LA. Bifurcation set in a system with homoclinic saddle curve. Math. Notes. 1990;28(6):910–916. DOI: 10.1007/BF01709154.
Received: 
06.06.2002
Accepted: 
12.05.2003
Available online: 
10.11.2023
Published: 
30.05.2003
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