Coexistence of Two Different Types of Intermittency near the Boundary of Phase Synchronization in the Presence of Noise

Intermittent behavior near the boundary of phase synchronization in the presence of noise is studied. In certain range of the coupling parameter and noise intensity the intermittency of eyelet and ring intermittencies is shown to take place. Main results are illustrated using the example of two unidirectional coupled Rössler systems. Similar behavior is shown to take place in two hydrodynamical models of Pierce diode coupled unidirectional.

Authors:

• Olga I. Moskalenko
• Maksim O. Zhuravlev
• Alexey A. Koronovskii
• Alexander E. Hramov

Keywords:

• Chaotic oscillators
• phase synchronization
• noise
• intermittency of intermittencies
• control.

References:

[1] P. Berge, Y. Pomeau, and C. Vidal, Order within Chaos, John Wiley and
Sons, New York, 1984.
[2] C. M. Kim, G. Yim, J. Ryu, and Y. Park, “Characteristic relations of
type III intermittency in an electronic circuit,” Phys. Rev. Lett., vol. 80,
no. 24, pp. 5317–5320, June 1998.
[3] J. L. Perez Velazquez and et al., “Type III intermittency in human partial
epilepsy,” European Journal of Neuroscience, vol. 11, pp. 2571–2576,
1999.
[4] I. Z. Kiss and J. L. Hudson, “Phase synchronization and suppression of
chaos through intermittency in forcing of an electrochemical oscillator,”
Phys. Rev. E, vol. 64, no. 4, pp. 046215, 2001.
[5] S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental
characterization of the transition to phase synchronization of chaotic
CO2 laser systems,” Phys. Rev. Lett., vol. 89, no. 19, pp. 194101, 2002.
[6] J. L. Cabrera and J. Milnor, “On-off intermittency in a human balancing
task,” Phys. Rev. Lett., vol. 89, no. 15, pp. 158702, 2002.
[7] A. E. Hramov, A. A. Koronovskii, I. S. Midzyanovskaya, E. Sitnikova,
and C. M. Rijn, “On-off intermittency in time series of spontaneous
paroxysmal activity in rats with genetic absence epilepsy,” Chaos, vol.
16, pp. 043111, 2006.
[8] E. Sitnikova, A. E. Hramov, V. V. Grubov, A. A. Ovchinnkov, and A.
A. Koronovsky, “Onoff intermittency of thalamo-cortical oscillations in
the electroencephalogram of rats with genetic predisposition to absence
epilepsy,” Brain Research, vol. 1436, pp. 147–156, 2012.
[9] M. Dubois, M. Rubio, and P. Berg´e, “Experimental evidence of
intermiasttencies associated with a subharmonic bifurcation,” Phys. Rev.
Lett., vol. 51, pp. 1446–1449, 1983.
[10] J. F. Heagy, N. Platt, and S. M. Hammel, “Characterization of on–off
intermittency,” Phys. Rev. E, vol. 49, no. 2, pp. 1140–1150, 1994.
[11] A. S. Pikovsky, G. V. Osipov, M. G. Rosenblum, M. Zaks, and J.
Kurths, “Attractor–repeller collision and eyelet intermittency at the
transition to phase synchronization,” Phys. Rev. Lett., vol. 79, no. 1, pp.
47–50, 1997.
[12] A. E. Hramov, A. A. Koronovskii, M. K. Kurovskaya, and S. Boccaletti,
“Ring intermittency in coupled chaotic oscillators at the boundary of
phase synchronization,” Phys. Rev. Lett., vol. 97, pp. 114101, 2006.
[13] A. E. Hramov, A. A. Koronovskii, O. I. Moskalenko, M. O. Zhuravlev,
V. I. Ponomarenko, and M. D. Prokhorov, “Intermittency of
intermittencies,” CHAOS, vol. 23, no. 3, pp. 033129, 2013.
[14] N. N. Nikitin, S. V. Pervachev, and V. D. Razevig, “About solution of
stochastic diferential equations of follow-up systems,” Automation and
telemechanics, vol. 4, pp. 133–137, 1975, in Russian.
[15] M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag
synchronization in coupled chaotic oscillators,” Phys. Rev. Lett., vol. 78,
no. 22, pp. 4193–4196, 1997.
[16] A. E. Hramov, A. A. Koronovskii, and M. K. Kurovskaya, “Two types
of phase synchronization destruction,” Phys. Rev. E, vol. 75, no. 3, pp.
036205, 2007.
[17] B. B. Godfrey, “Oscillatory nonlinear electron flow in Pierce diode,”
Phys. Fluids, vol. 30, pp. 1553, 1987.
[18] H. Matsumoto, H. Yokoyama, and D. Summers, “Computer simulations
of the chaotic dynamics of the Pierce beam–plasma system,” Phys.
Plasmas, vol. 3, no. 1, pp. 177, 1996.
[19] R. A. Filatov, A. E. Hramov, and A. A. Koronovskii, “Chaotic
synchronization in coupled spatially extended beam-plasma systems,”
Phys. Lett. A, vol. 358, pp. 301–308, 2006.
[20] P. J. Rouch, Computational fluid dynamics. Hermosa publishers,
Albuquerque, 1976.
[21] O. I. Moskalenko, A. A. Koronovskii, A. E. Hramov, and S. Boccaletti,
“Generalized synchronization in mutually coupled oscillators and
complex networks,” Phys. Rev. E, vol. 86, pp. 036216, 2012.
[22] A.E. Hramov, A.A. Koronovskii, “Detecting unstable periodic spatiotemporal
states of spatial extended chaotic systems”, Europhysics
Letters, vol. 80, pp. 10001, 2007.
[23] O. I. Moskalenko, A. A. Koronovskii, A. E. Hramov, M. O. Zhuravlev,
Yu. I. Levin, “Cooperation of deterministic and stochastic mechanisms
resulting in the intermittent behavior”, Chaos, Solitons & Fractals, vol.
68, pp. 58-64, 2014.