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


For citation:

Anishchenko V. S., Astakhov V. V., Vadivasova T. E., Strelkova G. I. Synchronization of regular, chaotic and stochastic fluctuations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 145-151.

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):
(downloads: 82)
Language: 
Russian
Heading: 
Article type: 
Other
UDC: 
534.1

Synchronization of regular, chaotic and stochastic fluctuations

Autors: 
Anishchenko Vadim Semenovich, Saratov State University
Astakhov Vladimir Vladimirovich, Yuri Gagarin State Technical University of Saratov
Vadivasova Tatjana Evgenevna, Saratov State University
Strelkova Galina Ivanovna, Saratov State University
Abstract: 

-

Key words: 
Reference: 
  1. Huygens H. Three memoirs on mechanics. Moscow: Publ. AS USSR; 1951. 370 p. (In Russian).
  2. Andronov AA. Collection of works. Moscow: Publ. AS USSR; 1956. 1956 p. (In Russian).
  3. Teodorchik KF. Self-oscillations systems. Moscow: Gostehizdat; 1952. 272 p. (In Russian).
  4. Hayashi C. Nonlinear oscillations in physical systems. Moscow: Mir; 1968. 424 p. (In Russian).
  5. Blehman II. Synchronizing Dynamic Systems. Moscow: Nauka; 1971. 894 p. (In Russian).
  6. Romanovsky YuM, Stepanova NV, Chernavsky DS. Mathematical models in biophysics. Moscow: Nauka; 1975. 343 p. (In Russian).
  7. Demyanchenko AG. Harmonic Oscillation Generator Synchronization. Moscow: Energia; 1976. 240 p. (In Russian).
  8. Winfree AT. The geometry of biological time. New York: Springer; 1980. 779 p.
  9. Landa PS. Self-oscillations in systems with finite number of degrees of freedom. Moscow : Nauka; 1980. 360 p. (In Russian).
  10. Blehman II. Synchronization in nature and technology. Moscow: Nauka; 1981. 351 p. (In Russian).
  11. Kuramoto Y. Chemical Oscillations Waves and Turbulence. Berlin: Springer; 1984. 158 p.
  12. Landa PS. Nonlinear oscillations and waves. Moscow: Fizmatlit; 1997. 496 p. (In Russian).
  13. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization. A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p. (In Russian).
  14. Anishchenko VS, Astakhov VV, Vadivasova TE, Neiman AB, Strelkova GI, Schimansky-Geier L. Nonlinear Effects in Chaotic and Stochastic Systems. Izhevsk-Moscow: Institute of Computer Sciences; 2003. (In Russian).
  15. Mosekilde E, Maistrenko Yu, Postnov D. Chaotic Synchronization. Applications to Living Systems. Singapore: World Scientific; 2002. 440 p.
  16. Matrosov VV, Shalfeev VD. Dynamic chaos in phase systems. Nizhny Novgorod: UNN Press; 2007. 255 p. (In Russian).
  17. Van der Poll B. Theory of the amplitude of free and forced triod vibration. Radio Rev. 1920;1:701–710.
  18. Appleton EV. The automatic synchronization of triode oscillator Proc. of the Cambridge Philosophical Society. Math. and Phys. Sciences. 1922;21:231–248.
  19. Andronov AA, Witt AA. To the mathematical theory of capture. Journal of Applied Physics. 1930;7(4):3–11.
  20. Mayer AG. To the theory of coupled oscillations of two self-excited generators. Vestnik GSU. 1935;2(5):3–11.
  21. Gaponov VI. Two connected generators with soft excitation. JTF. 1936;6(6):801–817 p.
  22. Teodorchik KF. To the theory of synchronization of relaxation self-oscillations. Dokl. Akad. Nauk SSSR. 1943;40(2):63–66.
  23. Khokhlov RV. To the theory of capture with a small amplitude of external force. Dokl. Akad. Nauk SSSR. 1954;97(3):411–414.
  24. Minakova II, Theodorchik KF. To the theory of synchronizing self-oscillations of an arbitrary form. Dokl. Akad. Nauk SSSR. 1956;106(4):658–660.
  25. Parygin VN. Mutual synchronization of three connected self-oscillating generators in case of weak communication.Radiotehnika i elektronika. 1956;1(2):197–204.
  26. Utkin GM. Mutual synchronization of generators at multiple frequencies Radiotehnika i elektronika. 1957;2(1):44–56.
  27. Stratonovich R L. Selected issues of the theory of fluctuations in radio engineering. Moscow: Sovet radio; 1961. 558 p. (In Russian).
  28. Malakhov AN. Fluctuations in self-oscillating systems. Moscow: Nauka; 1968. 660 p. (In Russian).
  29. Akopyan IG, Landa PS. Synchronization of self-oscillations on overtones in the presence of noise. Radiotehnika i elektronika. 1962;7(8):1285–1293.
  30. Kostin IK, Romanovsky YM. Fluctuations in the systems of many connected generators. Moscow University Physics Bulletin. 1972;13(6):698–705.
  31. Kostin IK, Romanovskii YM. Mutual synchronization of relaxation oscillators in the presence of noise. Radiophys Quantum Electron. 1975;18:23–26. DOI: 10.1007/BF01037654.
  32. Landa PS, Tarankova ND. Generator synchronization at modulation of its own frequency Radio Engineering and Electronic Physics. 1976;21(2):260–265.
  33. Skupoy VF, Kopylov VP. On synchronization of the FM-auto generator. Radio Engineering and Electronic Physics. 1979;24(7):1374–1379.
  34. Anishchenko V, Nikolaev S, Kurths J. Winding number locking on a twodimensional torus: Synchronization of quasiperiodic motions. Phys. Rev. E. 2006;73(5):056202. DOI: 10.1103/PhysRevE.73.056202.
  35. Anishchenko VS, Nikolaev SM. Experimental research of synchronization of two-frequency quasiperiodic motions. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(6):93–101. DOI: 10.18500/0869-6632-2007-15-6-93-101.
  36. Fujisaka H, Yamada Y. Stability theory of synchronized motions in coupled oscillatory syatems. Progr. Theor. Phys. 1983;69(1):32–47. DOI: 10.1143/PTP.69.32.
  37. Pikovsky AS. On the interaction of strange attractors. Z. Phys. B. 1984;55(2):149–154. DOI: 10.1007/BF01420567.
  38. Pikovsky AS. Synchronization of stochastic self-oscillations phase with periodic external signal. Journal of communications technology and electronics. 1985;1:1970–1974.
  39. Kuznetsov YuI, Landa PS, Olkhovoi AF, Perminov SM. On the relation between the synchronization amplitude threshold and entropy in the stochastic self-oscillatory systems. Dokl. Akad. Nauk SSSR. 1985;281(2):291–294.
  40. Afraimovich VS, Verichev NN, Rabinovich MI. Stochastic synchronization of oscillation in dissipative systems. Radiophys Quantum Electron. 1986;29:795–803. DOI: 10.1007/BF01034476.
  41. Pecora L, Carroll T. Synchronization of chaotic systems. Phys. Rev. Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
  42. Anishchenko VS, Postnov DE. Effect Of The Basic Frequency Locking Of Chaotic Auto-Oscillations - Synchronization Of Strange Attractors. Pisma v Zhurnal Tekhnicheskoi Fiziki. 1988;14(6):569–573.
  43. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Synchronization of chaos. International Journal of Bifurcation and Chaos. 1992;2(3):633-644. DOI: 10.1142/S0218127492000756.
  44. Rosenblum MG, Pikovsky A, Kurths J. Phase synchronization of chaotic oscillations. Phys. Rev. Lett. 1996;76(11):1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
  45. Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 1997;78:4193–4196. DOI: 10.1103/PHYSREVLETT.78.4193.
  46. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI. Generalized synchronization of chaos in unidirectorally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–995. DOI: 10.1103/physreve.51.980.
  47. Neiman AB. Synchronizationlike phenomena in coupled stochastic bistable systems. Phys. Rev. E. 1994;49(4):3484–3488. DOI: 10.1103/physreve.49.3484.
  48. Shulgin BV, Neiman AB, Anishchenko VS. Mean switching frequency locking in stochastic bistable systems driven by periodic force. Phys. Rev. Lett. 1995;75(23):4157–4160. DOI: 10.1103/PhysRevLett.75.4157.
  49. Anishchenko VS, Neiman AB, Moss F, Shimansky-Geier L. Stochastic resonance: noise-enhanced order. Phys. Usp. 1999;42:7–36. DOI: 10.1070/PU1999v042n01ABEH000444.
  50. Han SK, Yim TG, Postnov DE, Sosnovtseva OV. Interacting coherence resonance oscillators. Phys. Rev. Lett. 1999;83(9):1771–1774. DOI: 10.1103/PhysRevLett.83.1771.
  51. Doedel E, Paffenroth RC, Fairgrieve TF, Kuznetsov YA, Oldeman BE, Sandstede B, Wang X. AUTO2000: Continuation and bifurcation software for ordinary differential equations (with HOMCONT). Technical report, Concordia University; 2002.
Received: 
30.06.2009
Accepted: 
30.06.2009
Published: 
30.06.2009