Multifarious intertwined basin boundaries of strange nonchaotic attractors in a quasiperiodically forced system. (English) Zbl 1235.37013
Summary: A variety of different dynamical regimes involving strange nonchaotic attractors (SNAs) can be observed in a quasiperiodically forced delayed system. We describe some numerical experiments giving evidences of intertwined basin boundaries (smooth, non-Wada fractal and Wada property) for SNAs. In particular, we show that Wada property, fractality and smoothness can be intertwined on arbitrarily fine scales. This suggests that SNAs can exhibit the final state sensitivity and unpredictable behaviors. An interesting dynamical transition of SNAs together with associated mechanisms from non-Wada fractal to Wada intertwined basin boundaries is examined. A scaling exponent is used to characterize the intertwined basin boundaries.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
| 28A80 | Fractals |
| 68U20 | Simulation (MSC2010) |
| 65P20 | Numerical chaos |
Keywords:
strange nonchaotic attractors; unpredictability; intertwined basin boundaries; Wada propertyReferences:
| [1] | Grebogi, C.; Ott, E.; Yorke, J. A., Science, 238, 632 (1987) · Zbl 1226.37015 |
| [2] | Grebogi, C.; Ott, E.; Yorke, J. A., Phys. Rev. Lett., 56, 1011 (1986) |
| [3] | Nusse, H. E.; Yorke, J. A., Phys. Rev. Lett., 84, 626 (2000) |
| [4] | Nusse, H. E.; Yorke, J. A., Science, 271, 1376 (1996) · Zbl 1226.37009 |
| [5] | Sweet, D.; Ott, E.; Yorke, J. A., Nature, 399, 315 (1999) · Zbl 1369.37049 |
| [6] | Nusse, H. E.; Yorke, J. A., Physica D, 90, 242 (1996) · Zbl 0886.58072 |
| [7] | Poon, L.; Campos, J.; Ott, E.; Grebogi, C., Int. J. Bifur. Chaos, 6, 251 (1996) · Zbl 0870.58069 |
| [8] | Aguirre, J.; Viana, R. L.; Sanjuán, M. A.F., Rev. Mod. Phys., 81, 333 (2009) |
| [9] | Grebogi, C.; Ott, E.; Pelikan, S.; Yorke, J. A., Physica D, 13, 261 (1984) · Zbl 0588.58036 |
| [10] | Feudel, U.; Kuznetsov, S.; Pikovsky, A., Strange Nonchaotic Attractors (2006), World Scientific: World Scientific Singapore · Zbl 0989.37509 |
| [11] | Prasad, A.; Nandi, A.; Ramaswamy, R., Int. J. Bifur. Chaos, 17, 3397 (2007) · Zbl 1141.37308 |
| [12] | Prasad, A.; Negi, S. S.; Ramaswamy, R., Int. J. Bifur. Chaos, 11, 291 (2001) · Zbl 1090.37527 |
| [13] | Senthilkumar, D. V.; Srinivasan, K.; Thamilmaran, K.; Lakshmanan, M., Phys. Rev. E, 78, 066211 (2008) |
| [14] | Ruiz, G.; Parmananda, P., Phys. Lett. A, 367, 478 (2007) |
| [15] | Wang, X.; Zhan, M.; Lai, C.-H.; Lai, Y.-C., Phys. Rev. Lett., 92, 074102 (2004) |
| [16] | Kim, S. Y.; Lim, W.; Ott, E., Phys. Rev. E, 67, 056203 (2003) |
| [17] | Datta, S.; Ramaswamy, R.; Prasad, A., Phys. Rev. E, 70, 046203 (2004) |
| [18] | Lim, W.; Kim, S. Y., Phys. Lett. A, 355, 331 (2006) |
| [19] | Kim, S. Y.; Lim, W., Phys. Lett. A, 334, 160 (2005) · Zbl 1123.70321 |
| [20] | Aguirre, J.; Sanjuán, M. A.F., Physica D, 171, 41 (2002) · Zbl 1008.37011 |
| [21] | Breban, R.; Nusse, H. E., Physica D, 207, 52 (2005) · Zbl 1093.37012 |
| [22] | Zhang, Y.; Kong, G.; Yu, J.; Chu, Y., Phys. Lett. A, 372, 5979 (2008) · Zbl 1223.37044 |
| [23] | Zhang, Y.; Kong, G.; Yu, J., Phys. Lett. A, 373, 1341 (2009) · Zbl 1228.37029 |
| [24] | Grebogi, C.; Kostelich, E.; Ott, E.; Yorke, J. A., Physica D, 25, 347 (1987) |
| [25] | Grebogi, C.; McDonald, S. W.; Ott, E.; Yorke, J. A., Phys. Lett. A, 99, 415 (1983) |
| [26] | Yalcinkaya, T.; Lai, Y. C., Phys. Rev. Lett., 77, 5039 (1996) |
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