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Postnov D. E., Shishkin A. V., Sherbakov P. A. Nonlinear effects in ensembles of oscillators with resource distribution coupling. Part 2: oscillatory regimes of one-dimension array of self-sustained oscillators coupled via common power supply. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 5, pp. 23-35. DOI: 10.18500/0869-6632-2007-15-5-23-35

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Nonlinear effects in ensembles of oscillators with resource distribution coupling. Part 2: oscillatory regimes of one-dimension array of self-sustained oscillators coupled via common power supply

Postnov Dmitrij Engelevich, Saratov State University
Shishkin Aleksandr Vladislavovich, Saratov State University
Sherbakov Pavel Aleksandrovich, Saratov State University

We suggest the model of ensemble of resource sharing oscillators in the form of one-dimension array of self-sustained systems with N-type nonlinearity. We analyze the mechanism of oscillatory cluster formation, study the intra-cluster synchronization, and show the effect of energy fluctuations.

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  1. Postnov D.E., Sosnovtseva O.V. and Mosekilde E. Oscillator clustering in resource distribution chain // Chaos. 2005. Vol. 15. P. 1.
  2. Barfred M., Mosekilde E. and Holstein-Rathlou N.-H. Bifurcation analysis of nephron pressure and flow regulation // Chaos. 1996. Vol. 6. P. 280.
  3. Holstein-Rathlou N.-H. and Marsh D.J. A dynamic model of renal blood flow autoregulation // Bull. Math. Biol. 1994. Vol. 56. P. 441.
  4. Postnov D.E., Balanov A.G. and Mosekilde E. Synchronization phenomena in an array of population dynamic systems // Advances in Complex Systems. 1998. Vol. 1. P. 181.
  5. Mosekilde E., Maistrenko Yu. and Postnov D. Chaotic synchronization // Application to living systems. World Scientific, 2002.
  6. van der Pol B. and van der Mark J. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart // Phil. Mag. Suppl. 1928. Vol. 6. P. 763.
  7. Кузнецов А.П., Кузнецов С.П., Рыскин Н.М. Нелинейные колебания. Москва: Изд-во физ.-мат. литературы, 2002.
  8. FitzHugh R.A. Impulses and physiological states in theoretical models of nerve membrane // Biophys. J. 1961. Vol. 1. P. 445.
  9. Keener J., Sneyd J. Mathematical Physiology. New York: Springer-Verlag, 1998.
  10. Izhikevich Eugene M. Neural exctability, spiking and bursting // Int. J. Bifurcation and Chaos. 2000. Vol. 10, No 6. P. 1171.
  11. Pikovsky A. and Kurth J. Coherence resonance in a noise-driven excitable systems // Phys. Rev. Lett. 1997. Vol. 78. P. 775.
  12. Postnov D.E., Sosnovtseva O.V., Han S.K. and Kim W.S. Noise-induced multimode behavior in excitable systems // Phys. Rev. E. 2002. Vol. 66. P. 016203.
  13. Анищенко В.С., Нейман А.Б., Масс Ф., Шиманский-Гайер Л. Стохастический резонанс как индуцированный шумом эффект увеличения степени порядка // УФН. 1999. Т. 169, No 1. С. 7.
  14. Shulgin B.V., Neiman A.B. and Anishchenko V.S. Mean switching frequency locking in stochastic bistable systems driven by a periodic force // Phys. Rev. Lett. 1995. Vol. 75. P. 4157.
  15. Han S.K., Yim T.G., Postnov D.E., Sosnovtseva O.V. Interacting coherence resonance oscillators // Phys. Rev. Lett. 1999. Vol. 83. P. 1771.
  16. Postnov D., Han S.K., Yim T.G. and Sosnovtseva O. Experimental observation of coherence resonance in cascaded excitable systems // Phys. Rev. E. 1999. Vol. 59, No 4. P. 3791.
  17. Постнов Д.Э., Сосновцева О.В., Сецинский Д.В., Борисов В.С. Генерация и синхронизация стохастических колебаний в связанных возбудимых системах // Изв. вузов. ПНД. 2001. Т. 9, No 3.
  18. Сецинский Д.В., Постнов Д.Э. Индуцированная шумом когерентность в возбудимой системе с частотно-зависимой обратной связью // Письма в ЖТФ. 2005. Т. 31, вып. 7. C. 70.
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