×
Kocarev, Ljupčo; Tasev, Žarko; Stojanovski, Toni; Parlitz, Ulrich

Synchronizing spatiotemporal chaos. (English) Zbl 0934.37038

Chaos 7, No. 4, 635-643 (1997).
Summary: The authors show analytically and numerically that a pair of uni-directionally coupled spatially extended systems can synchronize. For the case of partial differential equations the synchronization can be achieved by applying the scalar driving signals only at finite number of space points. Their approach is very general and can be useful for practical applications since the synchronization is achieved via feeding in the response system only the information from certain (discrete) spatial locations of the drive system. Finally they stress some open problems in the field of synchronization of spatiotemporal chaos.

Cited in 14 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37K60 Lattice dynamics; integrable lattice equations

Keywords:

synchronize; driving signals; synchronization; open problems
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1103/RevModPhys.65.851 · Zbl 1371.37001 · doi:10.1103/RevModPhys.65.851
[2] Chua L. O., IEEE Trans. Circuits Syst. 42 pp 557– (1995)
[3] DOI: 10.1143/PTP.69.32 · Zbl 1171.70306 · doi:10.1143/PTP.69.32
[4] DOI: 10.1007/BF01034476 · doi:10.1007/BF01034476
[5] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821
[6] DOI: 10.1063/1.166278 · Zbl 0933.37030 · doi:10.1063/1.166278
[7] Perez Marino I., IEEE Trans. Circuits Syst. 42 pp 665– (1995) · doi:10.1109/81.473572
[8] Babloyantz A., Proc. Natl. Acad. Sci. USA 91 pp 9027– (1994) · doi:10.1073/pnas.91.19.9027
[9] Rees D., J. Fluid Mech. 221 pp 437– (1990) · Zbl 0686.76031 · doi:10.1017/S0022112090001641
[10] Joets A., J. Stat. Phys. 64 pp 981– (1991) · doi:10.1007/BF01048809
[11] Kocarev L., Phys. Rev. Lett. 77 pp 2206– (1996) · doi:10.1103/PhysRevLett.77.2206
[12] Kocarev L., Phys. Rev. Lett. 79 pp 51– (1997) · doi:10.1103/PhysRevLett.79.51
[13] DOI: 10.1103/PhysRevLett.76.1816 · doi:10.1103/PhysRevLett.76.1816
[14] DOI: 10.1103/PhysRevA.46.7387 · doi:10.1103/PhysRevA.46.7387
[15] Wu C., Int. J. Bifurcation Chaos 4 pp 979– (1994) · Zbl 0875.93445 · doi:10.1142/S0218127494000691
[16] DOI: 10.1103/PhysRevLett.74.5028 · doi:10.1103/PhysRevLett.74.5028
[17] Güémez J., Phys. Rev. E 52 pp R2145– (1995) · doi:10.1103/PhysRevE.52.R2145
[18] DOI: 10.1103/PhysRevE.53.4351 · doi:10.1103/PhysRevE.53.4351
[19] Feldmann U., Int. J. Circuit Theory Appl. 24 pp 551– (1996) · Zbl 0902.94005 · doi:10.1002/(SICI)1097-007X(199609/10)24:5<551::AID-CTA936>3.0.CO;2-H
[20] Konnur R., Phys. Rev. Lett. 77 pp 2937– (1996) · doi:10.1103/PhysRevLett.77.2937
[21] DOI: 10.1016/0375-9601(92)90745-8 · doi:10.1016/0375-9601(92)90745-8
[22] DOI: 10.1016/0375-9601(94)90114-7 · doi:10.1016/0375-9601(94)90114-7
[23] DOI: 10.1016/0375-9601(94)90947-4 · Zbl 0959.37508 · doi:10.1016/0375-9601(94)90947-4
[24] Hunt B. R., Phys. Rev. Lett. 76 pp 2254– (1996) · doi:10.1103/PhysRevLett.76.2254
[25] DOI: 10.1103/PhysRevLett.77.1751 · doi:10.1103/PhysRevLett.77.1751
[26] DOI: 10.1103/PhysRevLett.77.5361 · doi:10.1103/PhysRevLett.77.5361
[27] DOI: 10.1103/PhysRevLett.63.219 · doi:10.1103/PhysRevLett.63.219
[28] DOI: 10.1103/PhysRevLett.63.219 · doi:10.1103/PhysRevLett.63.219
[29] DOI: 10.1103/PhysRevLett.63.219 · doi:10.1103/PhysRevLett.63.219
[30] Chow S. N., Int. J. Bifurcation Chaos Appl. Sci. Eng. 6 pp 1605– (1996) · Zbl 1005.39504 · doi:10.1142/S0218127496000977
[31] Gray P., Chem. Eng. Sci. 39 pp 1087– (1989) · doi:10.1016/0009-2509(84)87017-7
[32] DeWitt A., Phys. Rev. E 48 pp R4191– (1993) · doi:10.1103/PhysRevE.48.R4191
[33] Rasmussen K. E., Int. J. Bifurcation Chaos Appl. Sci. Eng. 6 pp 1077– (1996) · Zbl 0881.92038 · doi:10.1142/S0218127496000588
[34] DOI: 10.1103/PhysRevE.50.1874 · doi:10.1103/PhysRevE.50.1874
[35] DOI: 10.1103/PhysRevLett.77.4162 · doi:10.1103/PhysRevLett.77.4162
[36] DOI: 10.1126/science.267.5199.868 · doi:10.1126/science.267.5199.868
[37] Skarda C., Behav. Brain Sci. 10 pp 170– (1987)
[38] DOI: 10.1146/annurev.ph.55.030193.002025 · doi:10.1146/annurev.ph.55.030193.002025
[39] DOI: 10.1103/PhysRevE.54.6708 · doi:10.1103/PhysRevE.54.6708
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.