zbMATH — the first resource for mathematics

Outer synchronization between drive-response networks with nonidentical nodes and unknown parameters. (English) Zbl 1258.34131
Summary: Through designing some proper controllers and adaptive updating laws, the outer synchronization between drive-response networks with nonidentical topological structure and unknown parameters are achieved and the unknown parameters are identified under given assumption. Several sufficient conditions for achieving outer synchronization are derived. Numerical simulations are provided to verify the effectiveness of the proposed methods.

34D06 Synchronization of solutions to ordinary differential equations
93C40 Adaptive control/observation systems
34H05 Control problems involving ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
Full Text: DOI
[1] Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998) · Zbl 1368.05139
[2] Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821–7826 (2002) · Zbl 1032.91716
[3] Albert, R., Jeong, H., Barabási, A.L.: Diameter of the world-wide web. Nature 401, 130–131 (1999)
[4] Williams, R.J., Martinez, N.D.: Simple rules yield complex food webs. Nature 404, 180–183 (2000)
[5] Kumpula, J.M., Onnela, J.P., Saramäki, J., Kaski, K., Kertész, J.: Emergence of communities in weighted networks. Phys. Rev. Lett. 99, 228701 (2007) · Zbl 1198.91181
[6] Chavez, M., Hwang, D.U., Amann, A., Hentschel, H.G.E., Boccaletti, S.: Synchronization is enhanced in weighted complex networks. Phys. Rev. Lett. 94, 218701 (2005)
[7] Lu, J., Ho, D.W.C., Kurths, J.: Consensus over directed static networks with arbitrary finite communication delays. Phys. Rev. E 80, 066121 (2009)
[8] Yang, M., Liu, Y., You, Z., Sheng, P.: Global synchronization for directed complex networks. Nonlinear Anal. 11, 2127–2135 (2010) · Zbl 1188.93095
[9] Mantegna, R.N.: Hierarchical structure in financial markets. Eur. Phys. J. B 11, 193–197 (1999)
[10] Chang, B.J., Hwang, R.H.: Modeling and analyzing the performance of adaptive hierarchical networks. Inf. Sci. 176, 522–549 (2006) · Zbl 05022817
[11] Wang, J., Wu, B., Wang, L., Fu, F.: Consensus of population systems with community structures. Phys. Rev. E 78, 051923 (2008)
[12] Wang, K., Fu, X., Li, K.: Cluster synchronization in community networks with nonidentical nodes. Chaos 19, 023106 (2009) · Zbl 1309.34107
[13] Li, C., Chen, G.: Synchronization in general complex dynamical networks with coupling delays. Physica A 343, 263–278 (2004)
[14] Guo, W., Chen, S., Austin, F.: Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling. Commun. Nonlinear Sci. Numer. Simul. 15, 1631–1639 (2010) · Zbl 1221.34213
[15] Xu, Y., Zhou, W., Fang, J., Sun, W.: Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling. Phys. Lett. A 374, 1673–1677 (2010) · Zbl 1236.05190
[16] Ghosh, D.: Projective-dual synchronization in delay dynamical systems with time-varying coupling delay. Nonlinear Dyn. (2011). doi: 10.1007/s11071-011-9945-1 · Zbl 1242.93055
[17] Rao, P., Wu, Z., Liu, M.: Adaptive projective synchronization of dynamical networks with distributed time delays. Nonlinear Dyn. (2011). doi: 10.1007/s11071-011-0100-9 · Zbl 1243.93059
[18] Zheng, S., Dong, G., Bi, Q.: Impulsive synchronization of complex networks with non-delayed and delayed coupling. Phys. Lett. A 373, 4255–4259 (2009) · Zbl 1234.05220
[19] Li, K., Lai, C.H.: Adaptive impulsive synchronization of uncertain complex dynamical networks. Phys. Lett. A 372, 1601–1606 (2008) · Zbl 1217.05210
[20] Guirey, E., Bees, M., Martin, A., Srokosz, M.: Persistence of cluster synchronization under the influence of advection. Phys. Rev. E 81, 051902 (2010)
[21] Lu, W., Liu, B., Chen, T.: Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos 20, 013120 (2010) · Zbl 1311.34117
[22] Li, C., Sun, W., Kurths, J.: Synchronization between two coupled complex networks. Phys. Rev. E 76, 046204 (2007)
[23] Wu, X., Zheng, W., Zhou, J.: Generalized outer synchronization between complex dynamical networks. Chaos 19, 013109 (2009) · Zbl 1311.34119
[24] Li, C., Xu, C., Sun, W., Xu, J., Kurths, J.: Outer synchronization of coupled discrete-time networks. Chaos 19, 013106 (2009) · Zbl 1311.34115
[25] Li, Z., Xue, X.: Outer synchronization of coupled networks using arbitrary coupling strength. Chaos 20, 023106 (2010) · Zbl 1311.34116
[26] Wang, G., Cao, J., Lu, J.: Outer synchronization between two nonidentical networks with circumstance noise. Physica A 389, 1480–1488 (2010)
[27] Wang, J., Ma, Q., Zeng, L., Abd-Elouahab, M.S.: Mixed outer synchronization of coupled complex networks with time-varying coupling delay. Chaos 21, 013121 (2011) · Zbl 1345.34102
[28] Yu, D., Righero, M., Kocarev, L.: Estimating topology of networks. Phys. Rev. Lett. 97, 188701 (2006)
[29] Zhou, J., Lu, J.: Topology identification of weighted complex dynamical networks. Physica A 386, 481–491 (2007)
[30] Ge, Z., Yang, C.: Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control. Physica D 231, 87–94 (2007) · Zbl 1167.34357
[31] Lü, L., Meng, L.: Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network. Nonlinear Dyn. (2011). doi: 10.1007/s11071-010-9927-8 · Zbl 1242.93035
[32] Yu, W., Cao, J.: Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Physica A 375, 467–482 (2007)
[33] Lorenz, E.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963) · Zbl 1417.37129
[34] Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465–1466 (1999) · Zbl 0962.37013
[35] Hassan, K.K.: Nonlinear Systems. Prentice Hall, Englewood Cliffs (2002) · Zbl 1003.34002
[36] Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999) · Zbl 1226.05223
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.