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Parameter identification of dynamical networks with community structure and multiple coupling delays. (English) Zbl 1222.93058
Summary: In many real systems, there exists community or hierarchical structure. When information or instruction transmits from one community to another or from one level to another, there may exist delays, i.e., the coupling delays between two nodes of different communities or layers. In view of this, chaotic dynamical networks with community structure and multiple coupling delays are studied in this paper. By viewing the coupling delays as unknown parameters, an approach based on synchronization is proposed to identify these unknown parameters. The sufficient conditions for the realization of parameter identification are obtained. Numerical examples verify the effectiveness of this method.

93B30 System identification
34K29 Inverse problems for functional-differential equations
37N35 Dynamical systems in control
05C82 Small world graphs, complex networks (graph-theoretic aspects)
91D30 Social networks; opinion dynamics
93C23 Control/observation systems governed by functional-differential equations
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, Michelle; 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] Yu, Dongchuan; Righero, Marco; Kocarev, Ljupco, Estimating topology of networks, Phys rev lett, 97, 188701, (2006)
[6] Zhou, Jin; Lu, Junan, Topology identification of weighted complex dynamical networks, Physica A, 386, 481-491, (2007)
[7] Ge, Zhengming; Yang, ChengHsiung, Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control, Physica D, 231, 87-94, (2007) · Zbl 1167.34357
[8] Liao, Teh-Lu; Lin, Sheng-Hung, Adaptive control and synchronization of Lorenz systems, J franklin inst, 336, 925-937, (1999) · Zbl 1051.93514
[9] Yu, Wenwu; Cao, Jinde, Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification, Physica A, 375, 467-482, (2007)
[10] Creveling, Daniel R.; Jeanne, James M.; Abarbanel, Henry D.I., Parameter estimation using balanced synchronization, Phys lett A, 372, 2043-2047, (2008)
[11] Grönlund, Andreas; Holme, Petter, Networking the seceder model: group formation in social and economic systems, Phys rev E, 70, 036108, (2004)
[12] González, M.C.; Herrmann, H.J.; Kertész, J.; Vicsek, T., Community structure and ethnic preferences in school friendship networks, Physica A, 379, 307-316, (2007)
[13] Zhou, Tao; Zhao, Ming; Chen, Guanrong; Yan, Gang; Wang, Bing-Hong, Phase synchronization on scale-free networks with community structure, Phys lett A, 368, 431-434, (2007)
[14] Arenas, Alex; Dı´az-Guiler, Albert; Pérez-Vicente, Conrad J., Synchronization processes in complex networks, Physica D, 224, 27-34, (2006) · Zbl 1112.34027
[15] Longtin, André; Milton, John G.; Bos, Jelte E.; Mackey, Michael C., Noise and critical behavior of the pupil light reflex at oscillation onset oscillation onset, Phys rev A, 41, 6992-7005, (1990)
[16] Luhta, Irma; Virtanen, Ilkka, Non-linear advertising capital model with time delayed feedback between advertising and stock of goodwill, Chaos solitons fractals, 7, 2083-2099, (1996)
[17] Peng, Haipeng; Li, Lixiang; Yang, Yixian; Zhang, Xiaohong, Parameter estimation of time-delay chaotic system, Chaos solitons fractals, (2007) · Zbl 1150.93339
[18] Cao, Jinde; Ho, Daniel W.C., A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach, Chaos solitons fractals, 24, 1317-1329, (2005) · Zbl 1072.92004
[19] Khalil, H.K., Nonlinear systems, (2002), Prentice Hall New Jersey
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