×

zbMATH — the first resource for mathematics

Persistent clusters in lattices of coupled nonidentical chaotic systems. (English) Zbl 1080.37525
Summary: Two-dimensional (2D) lattices of diffusively coupled chaotic oscillators are studied. In previous work, it was shown that various cluster synchronization regimes exist when the oscillators are identical. Here, analytical and numerical studies allow us to conclude that these cluster synchronization regimes persist when the chaotic oscillators have slightly different parameters. In the analytical approach, the stability of almost-perfect synchronization regimes is proved via the Lyapunov function method for a wide class of systems, and the synchronization error is estimated. Examples include a 2D lattice of nonidentical Lorenz systems with scalar diffusive coupling. In the numerical study, it is shown that in lattices of Lorenz and Rössler systems the cluster synchronization regimes are stable and robust against up to \(10\%-15\%\) parameter mismatch and against small noise.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1143/PTP.72.23 · Zbl 1074.37506
[2] DOI: 10.1143/PTP.72.23 · Zbl 1074.37506
[3] Afraimovich V.S., Izv. Vyssh. Uchebn. Zaved., Radiofiz. 29 pp 795– (1986)
[4] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019
[5] DOI: 10.1103/PhysRevE.50.1874
[6] DOI: 10.1103/PhysRevLett.74.4185
[7] DOI: 10.1063/1.166278 · Zbl 0933.37030
[8] DOI: 10.1103/PhysRevLett.80.2109
[9] DOI: 10.1109/81.904879 · Zbl 0994.82065
[10] DOI: 10.1016/0167-2789(92)90066-V · Zbl 0800.94342
[11] DOI: 10.1016/0167-2789(92)90066-V · Zbl 0800.94342
[12] DOI: 10.1016/0167-2789(92)90066-V · Zbl 0800.94342
[13] DOI: 10.1016/0167-2789(92)90066-V · Zbl 0800.94342
[14] Sherman A., Bull. Math. Biol. 56 pp 811– (1994)
[15] DOI: 10.1103/PhysRevE.58.6843
[16] DOI: 10.1103/PhysRevE.58.6843
[17] DOI: 10.1103/PhysRevE.58.6843
[18] DOI: 10.1103/PhysRevE.58.6843
[19] DOI: 10.1103/PhysRevE.59.4036
[20] DOI: 10.1103/PhysRevE.62.6332
[21] DOI: 10.1103/PhysRevE.63.036216
[22] DOI: 10.1016/S0167-2789(99)00193-1 · Zbl 0946.34041
[23] DOI: 10.1103/PhysRevE.53.4528
[24] DOI: 10.1103/PhysRevE.53.4528
[25] DOI: 10.1103/PhysRevE.53.4528
[26] DOI: 10.1103/PhysRevLett.76.1804
[27] DOI: 10.1103/PhysRevLett.78.4193
[28] DOI: 10.1103/PhysRevE.64.056228
[29] DOI: 10.1103/PhysRevE.64.056228
[30] DOI: 10.1103/PhysRevE.64.056228
[31] DOI: 10.1103/PhysRevE.64.056228
[32] DOI: 10.1088/0951-7715/9/3/006 · Zbl 0887.58034
[33] DOI: 10.1088/0951-7715/9/3/006 · Zbl 0887.58034
[34] DOI: 10.1088/0951-7715/9/3/006 · Zbl 0887.58034
[35] DOI: 10.1103/PhysRevE.52.R3313
[36] DOI: 10.1103/PhysRevE.52.R3313
[37] DOI: 10.1103/PhysRevE.52.R3313
[38] DOI: 10.1137/0150098 · Zbl 0712.92006
[39] DOI: 10.1038/scientificamerican1293-102
[40] DOI: 10.1103/PhysRevE.58.1764
[41] DOI: 10.1103/PhysRevE.63.016212
[42] DOI: 10.1109/81.633874
[43] DOI: 10.1103/PhysRevLett.80.3956
[44] DOI: 10.1103/PhysRevE.59.2817
[45] Yanchuk S., Int. J. Bifurcation Chaos Appl. Sci. Eng. 10 pp 2629– (2000)
[46] DOI: 10.1088/0951-7715/13/4/318 · Zbl 0957.37028
[47] DOI: 10.1016/S0167-2789(96)00276-X · Zbl 1194.34056
[48] DOI: 10.1080/02681119808806263 · Zbl 1067.34052
[49] DOI: 10.1142/S0218127400001778 · Zbl 0983.37018
[50] DOI: 10.1512/iumj.1972.21.21017
[51] DOI: 10.1142/S0218127401004078
[52] DOI: 10.1142/S0218127401004078
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.