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

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Kuznetsov A. P., Paksjutov V. I. Dynamics of the sprott’s coupled oscillators with nonidentical control parameters. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 3, pp. 95-106. DOI: 10.18500/0869-6632-2007-15-3-95-106

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Other
UDC: 
517.9
DOI: 
10.18500/0869-6632-2007-15-3-95-106

Dynamics of the sprott’s coupled oscillators with nonidentical control parameters

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Paksjutov Vladimir Igorevich, Saratov State University
Abstract: 

The structure of the plane of period-doubling control parameters is discussed for the set of coupled differential systems proposed by J. Sprott. It is shown, that the behavior of these systems may be both similar to one of the popular coupled Ressler system and different from it.

Key words: 
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Reference: 
  1. Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear dynamics of chaotic and stochastic systems. Fundamental principles and selected issues. Saratov: Saratov Univ. Publ.; 1999. 368 p.
  2. Mosekilde E, Maistrenko Y, Postnov D. Chaotic synchronization. Applications to living systems. World Scientific Series on Nonlinear Science, Series A. 2002;42:440.
  3. Jian-Min Yuan, Mingwhei Tung, Da Hsuan Feng, Lorenzo M. Narducci. Instability and irregular behaviour of coupled logistic equations. Phys. Rev. A. 1983;28(3):1662.
  4. Kuznetsov AP, Sedova JV, Sataev IR. Structure of control parameters space of nonidentical coupled systems with period-doublings. Izvestiya VUZ. Applied Nonlinear Dynamics. 2004;12(5):46–57.
  5. Reike C, Mosekilde E. Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems. Phys. Rev. E. 1995;52:1418–1435.
  6. Bezruchko BP, Prokhorov MD, Seleznev YeP. Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems. Chaos, Solitons and Fractals. 2003;15:695–711. DOI: 10.1016/S0960-0779(02)00171-6.
  7. Carvalho R, Fernandez B, Vilela Mendes R. From synchronization to multistability in two coupled quadratic maps. Physics Letters A. 2001;285:327-338.
  8. Hogg T, Huberman BA. Generic behaviour of coupled oscillators. Phys. Rev. A. 1984;29(1):275–281. DOI: 10.1103/PhysRevA.29.275.
  9. Sang-Yoon Kim, Hyungtae Kook. Period doubling in coupled maps. Phys. Rev. E. 1993;48(2):785–799. DOI: 10.1103/PhysRevE.48.785.
  10. Sang-Yoon Kim, Hyungtae Kook. Critical behaviour in coupled nonlinear systems. Phys. Rev. A. 1992;46(8):4467–4470. DOI: 10.1103/physreva.46.r4467.
  11. Rasmussen J, Mosekilde E, Reick C. Bifurcations in two coupled Ressler systems. Mathematics and Computers in Simulation. 1996;40:247–270. DOI: 10.1016/0378-4754(95)00036-4.
  12. Zhan M, Zheng Zg, Hu G, Peng Xh. Nonlocal chaotic phase synchronization. Phys. Rev. E. 2000;62(3):3552–7. DOI: 10.1103/physreve.62.3552.
  13. Hua-Wei Yin, Jian-Hua Dai, Hong-Jun Zhang. Phase effect of two coupled periodically driven Duffing oscillators. Phys. Rev. E. 1998;58(5):5683–5688.
  14. Kenfack А. Bifurcation structure of two coupled periodically driven double-well Duffing oscillators. Chaos, Solitons and Fractals. 2003;15:205. DOI: 10.1016/S0960-0779(01)00250-8.
  15. Rajasekar S, Murali K. Resonance behaviour and jump phenomenon in a two coupled Duffing–van der Pol oscillators. Chaos, Solitons and Fractals. 2004;19:925–934. DOI: 10.1016/S0960-0779(03)00277-7.
  16. Ivanchenko MV, Osipov GA, Shalfeev VD. Hierarchies of regular and chaotic synchronization in the system of coupled Ressler oscillators. Proceedings of the 6th Scientific Conference on Radiophysics, Nizhni Novgorod. 2002:114–115. (in Russian)
  17. Kuznetsov AP, Paksjutov VI. Features of the parameter plane of two nonidentical coupled Van der Pol – Duffing oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2005;13(4):3–19. DOI: 10.18500/0869-6632-2005-13-4-3-19.
  18. Kuznetsov AP, Paksjutov VI. Dynamics of two nonidentical coupled self-sustained systems with period doublings on the example of Rossler oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2006;14(2):3–15. DOI: 10.18500/0869-6632-2006-14-2-3-15.
  19. Kuznetsov AP, Paksyutov VI. Synchronization in non-identical control parameter coupled systems with period doubling bifurcations. Collection of materials of the scientific school-conference «Nonlinear days in Saratov for the young». Saratov: Publishing house of GOSUNTS «College»; 2005:126. (in Russian)
  20. Sprott JC. Some simple chaotic flows. Phys. Rev. E. 1994;50(2):647–650. DOI: 10.1103/physreve.50.r647.
  21. Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. (in Russian)
Received: 
01.02.2007
Accepted: 
09.04.2007
Published: 
29.06.2007
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