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)
The effect of control strength on the synchronization in pinning control questions. (English) Zbl 1219.93086
Summary: This paper investigates the effects of control strength on nonlinearly coupled systems in the process of synchronization, where the coupling strength is an invariable constant. Under the assumption of an asymmetric and reducible coupling matrix, two comparable sufficient conditions are obtained by using the Lyapunov direct method. Moreover, a rough bound for the control strength is presented. A simple simulation is also given to show the validity of the theorems. This work improves the current results that we have.
93C95Applications of control theory
34C15Nonlinear oscillations, coupled oscillators (ODE)
[1]Sorrentino, F.; Di Bernardo, M.; Garofalo, F.: Controllability of complex networks via pinning, Phys. rev. E 75, 046103 (2007)
[2]Boccaletti, S.; Latora, V.; Moreno, Y.: Complex networks: structure and dynamics, Phys. rep. 424, No. 4, 175-308 (2006)
[3]Xiang, J.; Chen, G. R.: On the V-stability of complex dynamical networks, Automatica 43, No. 6, 1049-1057 (2007)
[4]Chen, T. P.; Liu, X. W.; Lu, W. L.: Pinning complex networks by a single controller, IEEE trans. Circuits syst. I. regul. Pap. 54, No. 6, 1317-1326 (2007)
[5]De Lellis, P.; Di Bernardo, M.; Garofalo, F.: Synchronization of complex networks through local adaptive coupling, Chaos 18, No. 3, 037110 (2008)
[6]Xia, W. G.; Cao, J. D.: Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos 19, 013120 (2009)
[7]Zhou, J.; Wu, X. Q.; Yu, W. W.: Pinning synchronization of delayed neural networks, Chaos 18, 043111 (2008)
[8]Zhao, J. C.; Lu, J. A.; Wu, X. Q.: Pinning control of general complex dynamical networks with optimization, Sci. China inf. Sci. 53, 813-822 (2010)
[9]Zhang, Q. J.; Lu, J. A.; Zhao, J. C.: Impulsive synchronization of general continuous and discrete-time complex dynamical networks, Commun. nonlinear sci. Numer. simul. 15, 1063-1070 (2010) · Zbl 1221.93107 · doi:10.1016/j.cnsns.2009.05.048
[10]Tang, Y.; Wang, Z. D.; Fang, J. A.: Pinning control of fractional-order weighted complex networks, Chaos 19, 013112 (2009)
[11]Wu, C. W.: Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling, IEEE trans. Circuits syst. II 52, 282-286 (2005)
[12]Liu, X. W.; Chen, T. P.; Lu, W. L.: Consensus problem in directed networks of multi-agents via nonlinear protocols, Phys. lett. A 373, 3122-3127 (2009) · Zbl 1233.34012 · doi:10.1016/j.physleta.2009.06.054
[13]Wu, C. W.; Chua, L. O.: Synchronization in an array of linearly coupled dynamical systems, IEEE trans. Circuits syst. I 42, 430-447 (1995) · Zbl 0867.93042 · doi:10.1109/81.404047