zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Synchronization criteria and pinning control of general complex networks with time delay. (Synchronization criterions and pinning control of general complex networks with time delay.) (English) Zbl 1188.34100
The problem of synchronization for general time-delay complex dynamical networks is investigated. Some new and less conservative conditions are obtained for both continuous-time and discrete-time cases, which guarantee the synchronized states to be asymptotically stable. These conditions are converted to LMIs. Some numerical examples are presented.
MSC:
34K20Stability theory of functional-differential equations
34K35Functional-differential equations connected with control problems
References:
[1]Strogatz, S. H.: Exploring complex networks, Nature 410, 268-276 (2001)
[2]Barabási, A. L.; Albert, R.: Emergence of scaling in random networks, Science 286, 509-512 (1999) · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[3]Dorogovtesev, S. N.; Mendes, J. F. F.: Evolution of networks, Advances in physics 51, 1079-1187 (2002)
[4]Newman, M. E. J.: The structure and function of complex networks, SIAM review 45, 167 (2003) · Zbl 1029.68010 · doi:10.1137/S003614450342480
[5]Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D. -U.: Complex networks: structure and dynamics, Physics reports 424, 175-308 (2006)
[6]Erdös, P.; Rényi, A.: On the evolution of random graphs-II, Bulletin of the international statistical institute 38, 343 (1961) · Zbl 0106.12006
[7]Watts, D. J.; Strogatz, S. H.: Collective dynamics of small-world networks, Nature 393, 440-442 (1998)
[8]Pecora, L. M.; Carroll, T. L.: Master stability functions for synchronized coupled systems, Physics review letters 80, 2109-2112 (1998)
[9]Fink, K. S.; Johnson, G.; Carroll, T.; Mar, D.; Pecora, L.: Three coupled oscillator as a universal probe of synchronization stability in coupled oscillator arrays, Physics review E 61, 5080 (2000)
[10]Yin, C.; Wang, W.; Chen, G.; Wang, B.: Decoupling process for better synchronizability on scale-free networks, Physics review E 74, 047102 (2006)
[11]Hong, H.; Kim, B. J.; Choi, M. Y.; Park, H.: Factors that predict better synchronizability on complex networks, Physics review E 69, 067105 (2004)
[12]Hwang, D.; Chavez, M.; Amann, A.; Boccaletti, S.: Synchronization in complex networks with age ordering, Physics review letters 94, 138701 (2005)
[13]Colizza, V.; Banavar, J. R.; Maritan, A.; Rinaldo, A.: Network structures from selection principles, Physics review letters 92, 198701 (2004)
[14]Lü, J.; Zhou, T.; Zhang, S.: Chaos synchronization between linearly coupled chaotic system, Chaos solitons & fractals 14, 529-541 (2002) · Zbl 1067.37043 · doi:10.1016/S0960-0779(02)00005-X
[15]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Physics review letters 64, 821-824 (1990)
[16]Albert, R.; Barabási, A. L.: Statistical mechanics of complex networks, Review of modern physics 74, 47 (2002) · Zbl 1205.82086 · doi:10.1103/RevModPhys.74.47
[17]Jr., J. S. Andrade; Bezerra, D. M.; Filho, J. Ribeiro; Moreira, A. A.: The complex topology of chemical plants, Physica A 360, 637-643 (2006)
[18]Donetti, L.; Hurtado, P.; Muñoz, M. A.: Entangled networks synchronization and optimal network topology, Physics review letters 95, 188701 (2005)
[19]Chen, M. Y.: Synchronization in time-varying networks: a matrix measure approach, Physics review E 76, 016104 (2007)
[20]Wang, X. F.; Chen, G.: Pinning control of scale-free dynamical networks, Physica A 310, 521-531 (2002) · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[21]Wang, X. F.; Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility, IEEE transactions on circuits and systems-I 49, 54-62 (2002)
[22]Wang, X. F.; Chen, G.: Synchronization in small-world dynamical networks, International journal of bifurcation and chaos 9, 1435-1442 (2002)
[23]Li, C. G.; Chen, G.: Synchronization in general complex dynamical networks with coupling delays, Physica A 343, 263-278 (2004)
[24]Wang, L.; Dai, H. P.; Sun, Y. X.: Synchronization criteria for a generalized complex delayed dynamical network model, Physica A 383, 703-713 (2007)
[25]Almaas, E.; Kovács, B.; Vicsek, T.; Oltvai, Z. N.; Barabási, A. -L.: Global organization of metabolic fluxes in the bacterium escherichia coli, Nature 427, 839-843 (2004)
[26]Gao, H. J.; Lam, J.; Chen, G.: New criteria for synchronization stability of general complex dynamical networks with coupling delays, Physica letter A 360, 263 (2006)
[27]Li, X.; Chen, G.: Pinning a complex dynamical networks to its equilibrium, IEEE transactions on circuits and systems-I 51, 2074-2087 (2004)
[28]Liu, Z. X.; Chen, Z. Q.; Yuan, Z. Z.: Pinning control of weighted general complex dynamical networks with time delay, Physica A 375, 345-354 (2007)
[29]Moon, Y. M.; Park, P.; Kwon, W. H.; Lee, Y. S.: Delay-dependent robust stabilization of uncertain state-delayed systems, International journal of control 74, No. 14, 1447-1455 (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116