zbMATH — the first resource for mathematics

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. (English) Zbl 1223.90013
Summary: In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ’delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.

90B15 Stochastic network models in operations research
05C82 Small world graphs, complex networks (graph-theoretic aspects)
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
34K50 Stochastic functional-differential equations
37H10 Generation, random and stochastic difference and differential equations
37B25 Stability of topological dynamical systems
LMI toolbox; Matlab
Full Text: DOI
[1] Dangalchev, C., Physica A, 338, 659, (2004)
[2] Duan, Z.; Chen, G.; Huang, L., Phys. lett. A, 372, 3741, (2008)
[3] Gao, H.; Lam, J.; Chen, G., Phys. lett. A, 360, 263, (2006)
[4] Li, Z.; Chen, G., IEEE trans. circuits syst.-II, 53, 28, (2006)
[5] Lu, W.; Chen, T., Physica D, 198, 148, (2004)
[6] Strogatz, S., Nature, 410, 268, (2001)
[7] Toroczkai, Z., Los alamos sci., 29, 94, (2005)
[8] Wang, X.; Chen, G., IEEE circuits syst. mag., 3, 6, (2003)
[9] Yan, J.J.; Chang, W.D.; Hung, M.L., Chaos solitons fractals, 29, 506, (2006)
[10] Yu, W.; Cao, J.; Lu, J., SIAM J. appl. dyn. syst., 7, 108, (2008)
[11] Hua, C.; Wang, Q.; Guan, X., Phys. lett. A, 368, 281, (2007)
[12] Li, C.P.; Sun, W.G.; Kurths, J., Physica A, 361, 24, (2006)
[13] Li, Z.; Lee, J., Physica A, 387, 1369, (2008)
[14] Liu, X.; Chen, T., Physica A, 381, 82, (2007)
[15] Wang, Z.; Liu, Y.; Li, M.; Liu, X., IEEE trans. neural networks, 17, 814, (2006)
[16] Gao, H.; Chen, T., IEEE trans. automat. control, 53, 655, (2008)
[17] Liang, J.; Wang, Z.; Liu, X., Nonlinear dyn., 53, 153, (2008)
[18] Liang, J.; Wang, Z.; Liu, Y.; Liu, X., IEEE trans. syst. man cybernetics B, 38, 1073, (2008)
[19] Sun, Y.; Cao, J.; Wang, Z., Neurocomputing, 70, 2477, (2007)
[20] Wang, W.; Cao, J., Physica A, 366, 197, (2006)
[21] Wang, Z.; Shu, H.; Fang, J.; Liu, X., Nonlinear anal. real world appl., 7, 1119, (2006)
[22] Mou, S.; Gao, H.; Qiang, W.; Chen, K., IEEE trans. syst. man cybernetics B, 38, 571, (2008)
[23] Mou, S.; Zhao, Y.; Gao, H.; Qiang, W., Int. J. comput. math., 8, 1255, (2008)
[24] Langville, A.N.; Stewart, W.J., J. comput. appl. math., 167, 429, (2004)
[25] Arnold, L., Random dynamical systems, (1998), Springer-Verlag Berlin
[26] Khasminskii, R.Z., Stochastic stability of differential equations, (1980), Alphen aan den Rijn, Sijthoffand Noor Khasminskiidhoff · Zbl 1259.60058
[27] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia · Zbl 0816.93004
[28] Liu, Y.; Wang, Z.; Liu, X., Neural networks, 19, 667, (2006)
[29] Gu, K.Q.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhauser Boston · Zbl 1039.34067
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.