zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

93B30System identification
34K29Inverse problems in theory of functional-differential equations
37N35Dynamical systems in control
05C82Small world graphs, complex networks (graph theory)
91D30Social networks
93C23Systems 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)
[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 · doi:10.1073/pnas.122653799 · http://www.pnas.org/content/vol99/issue12/#APPLIED_MATHEMATICS
[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 · doi:10.1016/j.physd.2007.03.019
[8] Liao, Teh-Lu; Lin, Sheng-Hung: Adaptive control and synchronization of Lorenz systems, J franklin inst 336, 925-937 (1999) · Zbl 1051.93514 · doi:10.1016/S0016-0032(99)00010-1
[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) · Zbl 1163.37386
[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&acute, Albert; Az-Guiler; 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 · doi:10.1016/j.chaos.2004.09.063
[19] Khalil, H. K.: Nonlinear systems, (2002) · Zbl 1003.34002