×

Analytical and numerical studies of noise-induced synchronization of chaotic systems. (English) Zbl 0983.65135

Summary: We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.

MSC:

65P20 Numerical chaos
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] DOI: 10.1088/0305-4470/14/11/006
[2] DOI: 10.1111/j.2153-3490.1981.tb01746.x
[3] DOI: 10.1103/RevModPhys.70.223
[4] DOI: 10.1103/PhysRevLett.81.4012
[5] DOI: 10.1103/PhysRevLett.71.807
[6] DOI: 10.1103/PhysRevE.50.3249
[7] DOI: 10.1103/PhysRevLett.78.775 · Zbl 0961.70506
[8] DOI: 10.1103/PhysRevE.61.6103
[9] DOI: 10.1103/PhysRevLett.71.1542
[10] DOI: 10.1016/0378-4371(95)00350-9
[11] DOI: 10.1103/PhysRevLett.73.3395
[12] DOI: 10.1103/PhysRevLett.73.3395
[13] DOI: 10.1103/PhysRevE.54.6918
[14] DOI: 10.1103/PhysRevLett.79.2389
[15] DOI: 10.1103/PhysRevLett.79.2389
[16] DOI: 10.1209/epl/i1998-00217-9
[17] DOI: 10.1103/PhysRevE.60.3597
[18] DOI: 10.1103/PhysRevLett.74.2134
[19] DOI: 10.1103/PhysRevLett.76.2609
[20] DOI: 10.1007/BF01044729
[21] DOI: 10.1103/PhysRevLett.79.3633
[22] DOI: 10.1103/PhysRevLett.79.3633
[23] DOI: 10.1103/PhysRevLett.85.227
[24] C. Palenzuela, R. Toral, C. R. Mirasso, O. Calvo, and J. D. Gunton, preprint cond-mat/0007371.
[25] DOI: 10.1103/PhysRevE.55.4804
[26] DOI: 10.1103/PhysRevE.61.3230
[27] DOI: 10.1103/PhysRevE.58.R6907
[28] DOI: 10.1016/S0167-2789(98)00259-0 · Zbl 1065.94567
[29] DOI: 10.1063/1.166344 · Zbl 0994.94023
[30] DOI: 10.1007/BF01010923
[31] DOI: 10.1103/PhysRevLett.65.2935 · Zbl 1050.37515
[32] DOI: 10.1103/PhysRevLett.69.761
[33] DOI: 10.1103/PhysRevE.52.2091
[34] DOI: 10.1103/PhysRevLett.77.4318
[35] DOI: 10.1142/S0218127499000365 · Zbl 0972.37507
[36] DOI: 10.1016/0375-9601(92)91049-W
[37] DOI: 10.1103/PhysRevLett.72.1451
[38] DOI: 10.1103/PhysRevLett.73.2932
[39] DOI: 10.1103/PhysRevLett.73.2932
[40] DOI: 10.1103/PhysRevE.54.R2201
[41] DOI: 10.1103/PhysRevE.58.5188
[42] DOI: 10.1103/PhysRevE.56.2272
[43] DOI: 10.1103/PhysRevE.52.3238
[44] DOI: 10.1103/PhysRevE.53.6551
[45] DOI: 10.1016/0375-9601(96)00306-4
[46] DOI: 10.1103/PhysRevE.56.4068
[47] DOI: 10.1103/PhysRevE.60.2779
[48] DOI: 10.1142/S0218127499001826
[49] DOI: 10.1209/epl/i1998-00368-1
[50] DOI: 10.1103/PhysRevE.53.2087
[51] DOI: 10.1016/S0167-2789(98)00247-4 · Zbl 1038.37515
[52] DOI: 10.1016/S0167-2789(98)00247-4 · Zbl 1038.37515
[53] DOI: 10.1016/S0167-2789(98)00247-4 · Zbl 1038.37515
[54] DOI: 10.1016/S0375-9601(98)00799-3
[55] DOI: 10.1103/PhysRevLett.85.5456
[56] DOI: 10.1063/1.1371285
[57] DOI: 10.1103/PhysRevLett.85.2304
[58] L. Baroni, R. Livi, and A. Torcini, preprint chao-dyn/9907005;
[59] DOI: 10.1103/PhysRevE.63.036226
[60] DOI: 10.1016/0010-4655(93)90016-6 · Zbl 0854.65005
[61] DOI: 10.1103/PhysRevE.60.1648
[62] DOI: 10.1103/PhysRevLett.77.5361
[63] DOI: 10.1103/PhysRevLett.77.5361
[64] DOI: 10.1103/PhysRevLett.77.5361
[65] DOI: 10.1103/PhysRevLett.77.5361
[66] DOI: 10.1103/PhysRevLett.72.3498
[67] DOI: 10.1103/PhysRevLett.72.3498
[68] DOI: 10.1103/PhysRevLett.72.3498
[69] DOI: 10.1103/PhysRevLett.72.3498
[70] DOI: 10.1103/PhysRevLett.72.3498
[71] DOI: 10.1103/PhysRevLett.72.3498
[72] DOI: 10.1103/PhysRevLett.76.1804
[73] DOI: 10.1103/PhysRevLett.78.4379
[74] DOI: 10.1103/PhysRevE.59.R2520
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.