Previous |  Up |  Next


on-off intermittency; Chen system; Blowout bifurcation; intermingled basin; power law
Previous studies on on-off intermittency in continuum systems are generally based on the synchronization of identical chaotic oscillators or in nonlinear systems driven by the Duffing oscillator. In this paper, one-state on-off intermittency and two-state on-off intermittency are observed in two five- dimensional continuum systems, respectively, where each system has a two- dimensional subsystem driven by the chaotic Chen system. The phenomenon of intermingled basins is observed below the blowout bifurcation. Basic statistical properties of the intermittency are investigated. It is shown that the distribution of the laminar phase follows a -3/2 power law, and that of the burst amplitudes follows a -1 power law, consistent with the basic statistical characteristics of on-off intermittency.
[1] Ashwin P., Covas, E., Tavakol R.: Transverse instability for non-normal parameters. Nonlinearity 12 (1999), 563–577 MR 1690194 | Zbl 0984.37053
[2] Bickel D. R.: Estimating the intermittency of point processes with applications to human activity and viral DNA. Phys. A 265 (1999), 634–648
[3] Cabrera J. L., Milton J. G.: On-off intermittency in a human balancing task. Phys. Rev. Lett. 89 (2002), 1587021–1587024
[4] Velho H. F. Campos, Rosa R. R., Ramos F. M., Sr R. A. Pielke, Degrazia G. A.: Representing intermittency in turbulent fluxes: An application to the stable atmospheric boundary layer. Phys. A 354 (2005), 88–94
[5] Cenys A., Anagnostopoulos A. N., Bleris G. L.: Symmetry between laminar and burst phases for on-off intermittency. Phys. Rev. E 56 (1997), 2592–2596
[6] Chen G., Ueta T.: Yet another chaotic attractor. Internat. J. Bifur. Chaos 9 (1999), 1465-1466 MR 1729683 | Zbl 0962.37013
[7] Grebogi C., Ott E., Romeiras, F., Yorke J. A.: Critical exponents for crisis induced intermittency. Phys. Rev. A 36 (1987), 5365–5379 MR 0919537
[8] Harnos A., Horváth G., Lawrence A. B., Vattay G.: Scaling and intermittency in animal behavior. Phys. A 286 (2000), 312–320
[9] Heagy J. F., Platt, N., Hammel S. M.: Characterization of on-off. Intermittency. Phys. Rev. E 49 (1994), 1140–1150
[10] Hramov A. E., Koronovskii A. A., Midzyanovskaya I. S., Sitnikova, E., Rijn C. M. van: On-off intermittency in time series of spontaneous paroxysmal activity in rats with genetic absence epilepsy. Chaos 16 (2006), 0431111–0431117
[11] Kim C.-M.: Mechanism of chaos synchronization and on-off intermittency. Phys. Rev. E 56 (1997), 3697–3700
[12] Lai Y.-C., Grebogi C.: Intermingled basins and two-state on-off intermittency. Phys. Rev. E 52 (1995), 3313–3316
[13] Lippiello E., Arcangelis, L. de, Godano C.: On-off intermittency in mean-field earthquake model. Europhys. Lett. 76 (2006), 979–985
[14] Núñez M.: Rigorous bounds on intermittent bursts for turbulent flows. Phys. D 176 (2003), 237–241 MR 1965379 | Zbl 1036.76022
[15] Ott E., Sommerer J. C.: Blowout bifurcations: The occurrence of riddled basins. Phys. Lett. A 188 (1994), 39–47
[16] Platt N., Hammel S. M., Heagy J. F.: Effects of additive noise on on-off intermittency. Phys. Rev. Lett. 72 (1994), 3498–3501
[17] Platt N., Spiegel E. A., Tresser C.: On-off Intermittency: A mechanism for bursting. Phys. Rev. Lett. 70 (1993), 279–282
[18] Pomeau Y., Manneville P.: Intermittent transition to turbulence in dissipative dynamical systems. Comm. Math. Phys. 74 (1980), 189–197 MR 0576270
[19] Stefański A., Kapitaniak T., Brindley, J., Astakhov V.: Torus on-off intermittency in coupled Lorenz systems. Phys. Rev. E 57 (1998), 1175–1177
[20] Toniolo C., Provenzale, A., Spiegel E. A.: Signature of on-off intermittency in measured signals. Phys. Rev. E 66 (2002), 066209
[21] Venkataramani S. C., Jr. T. M. Antonsen, Ott, E., Sommerer J. C.: On-off fractal properties of time series. Phys. D 96 (1994), 66–99
[22] Zhan M., Hu, G., Yang J. Z.: Synchronization of chaos in coupled systems. Phys. Rev. E 62 (2000), 2963–2966
Partner of
EuDML logo