Generalized outer synchronization between complex dynamical networks. (English) Zbl 1311.34119
Summary: In this paper, the problem of generalized outer synchronization between two completely different complex dynamical networks is investigated. With a nonlinear control scheme, a sufficient criterion for this generalized outer synchronization is derived based on Barbalat’s lemma. Two corollaries are also obtained, which contains the situations studied in two lately published papers as special cases. Numerical simulations further demonstrate the feasibility and effectiveness of the theoretical results.{
©2009 American Institute of Physics}
©2009 American Institute of Physics}
MSC:
34D06 | Synchronization of solutions to ordinary differential equations |
05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
37N35 | Dynamical systems in control |
References:
[1] | DOI: 10.1038/30918 · Zbl 1368.05139 · doi:10.1038/30918 |
[2] | DOI: 10.1038/35065725 · Zbl 1370.90052 · doi:10.1038/35065725 |
[3] | DOI: 10.1016/S0378-4371(99)00291-5 · doi:10.1016/S0378-4371(99)00291-5 |
[4] | DOI: 10.1038/35036627 · doi:10.1038/35036627 |
[5] | DOI: 10.1093/bioinformatics/14.7.591 · doi:10.1093/bioinformatics/14.7.591 |
[6] | DOI: 10.1093/bioinformatics/bth199 · doi:10.1093/bioinformatics/bth199 |
[7] | DOI: 10.1103/PhysRevLett.80.2109 · doi:10.1103/PhysRevLett.80.2109 |
[8] | DOI: 10.1103/PhysRevLett.89.054101 · doi:10.1103/PhysRevLett.89.054101 |
[9] | DOI: 10.1103/PhysRevE.67.026209 · doi:10.1103/PhysRevE.67.026209 |
[10] | DOI: 10.1109/81.404047 · Zbl 0867.93042 · doi:10.1109/81.404047 |
[11] | DOI: 10.1109/81.956024 · Zbl 0999.94577 · doi:10.1109/81.956024 |
[12] | DOI: 10.1109/TCSI.2002.808215 · Zbl 1368.34051 · doi:10.1109/TCSI.2002.808215 |
[13] | Wu C. W., IEEE Trans. Circuits Syst., I: Regul. Pap. 52 pp 282– (2005) · doi:10.1109/TCSII.2005.846884 |
[14] | DOI: 10.1142/4777 · doi:10.1142/4777 |
[15] | DOI: 10.1109/81.974874 · Zbl 1368.93576 · doi:10.1109/81.974874 |
[16] | DOI: 10.1142/S0218127402004292 · doi:10.1142/S0218127402004292 |
[17] | DOI: 10.1109/TAC.2005.849233 · Zbl 1365.93406 · doi:10.1109/TAC.2005.849233 |
[18] | DOI: 10.1109/TAC.2006.872760 · Zbl 1366.93544 · doi:10.1109/TAC.2006.872760 |
[19] | DOI: 10.1063/1.2737829 · Zbl 1159.37366 · doi:10.1063/1.2737829 |
[20] | DOI: 10.1103/PhysRevE.76.046204 · doi:10.1103/PhysRevE.76.046204 |
[21] | DOI: 10.1016/j.physa.2008.05.047 · doi:10.1016/j.physa.2008.05.047 |
[22] | DOI: 10.1103/PhysRevE.51.980 · doi:10.1103/PhysRevE.51.980 |
[23] | DOI: 10.1103/PhysRevLett.76.1816 · doi:10.1103/PhysRevLett.76.1816 |
[24] | DOI: 10.1063/1.2903841 · Zbl 1307.34079 · doi:10.1063/1.2903841 |
[25] | DOI: 10.1063/1.2911541 · doi:10.1063/1.2911541 |
[26] | DOI: 10.1137/1031127 · Zbl 0687.15010 · doi:10.1137/1031127 |
[27] | Khalil H. K., Nonlinear Systems, 3. ed. (2002) |
[28] | DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 |
[29] | DOI: 10.1016/S0960-0779(00)00216-2 · Zbl 1073.93537 · doi:10.1016/S0960-0779(00)00216-2 |
[30] | DOI: 10.1038/35023206 · doi:10.1038/35023206 |
[31] | DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 · doi:10.1142/S0218127499001024 |
[32] | DOI: 10.1142/S0218127402005224 · doi:10.1142/S0218127402005224 |
[33] | DOI: 10.1142/S0218127402004851 · Zbl 1044.37021 · doi:10.1142/S0218127402004851 |
[34] | DOI: 10.1142/S021812740200631X · Zbl 1043.37026 · doi:10.1142/S021812740200631X |
[35] | DOI: 10.1016/0375-9601(79)90150-6 · Zbl 0996.37502 · doi:10.1016/0375-9601(79)90150-6 |
[36] | DOI: 10.1103/PhysRevA.41.3826 · doi:10.1103/PhysRevA.41.3826 |
[37] | DOI: 10.1142/S0218127494000356 · Zbl 0813.58037 · doi:10.1142/S0218127494000356 |
[38] | DOI: 10.1142/S0218127405013988 · doi:10.1142/S0218127405013988 |
[39] | DOI: 10.1016/j.physa.2005.09.039 · doi:10.1016/j.physa.2005.09.039 |
[40] | DOI: 10.1016/j.jmaa.2005.11.008 · Zbl 1104.37024 · doi:10.1016/j.jmaa.2005.11.008 |
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