Lu, Jianquan; Ho, Daniel W. C.; Cao, Jinde Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling. (English) Zbl 1165.34414 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 10, 3101-3111 (2008). Summary: A general complex dynamical network consisting of \(N\) nonlinearly coupled identical chaotic neural networks with coupling delays is firstly formulated. Many studied models with coupling systems are special cases of this model. Synchronization in such dynamical network is considered. Based on the Lyapunov–Krasovskii stability theorem, some simple controllers with updated feedback strength are introduced to make the network synchronized. The update gain \(\gamma_i\) can be properly chosen to make some important nodes synchronized quicker or slower than the rest. Two examples including nearest-neighbor coupled networks and scale-free network are given to verify the validity and effectiveness of the proposed control scheme. Cited in 23 Documents MSC: 34K25 Asymptotic theory of functional-differential equations 34K23 Complex (chaotic) behavior of solutions to functional-differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics Keywords:synchronization; chaotic neural networks; complex networks; delay coupling PDFBibTeX XMLCite \textit{J. Lu} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 10, 3101--3111 (2008; Zbl 1165.34414) Full Text: DOI References: [1] Barabási A., Science 286 pp 509– · Zbl 1353.94001 [2] DOI: 10.1103/PhysRevLett.89.054101 [3] DOI: 10.1016/S0370-1573(02)00137-0 · Zbl 0995.37022 [4] DOI: 10.1016/j.chaos.2004.09.063 · Zbl 1072.92004 [5] DOI: 10.1016/j.physleta.2005.12.092 [6] DOI: 10.1063/1.2178448 · Zbl 1144.37331 [7] DOI: 10.1142/S0218127404010655 · Zbl 1077.37506 [8] DOI: 10.1063/1.2126581 · Zbl 1144.37338 [9] DOI: 10.1073/pnas.81.10.3088 · Zbl 1371.92015 [10] DOI: 10.1103/PhysRevE.71.037203 [11] DOI: 10.1103/PhysRevLett.94.138701 [12] DOI: 10.1103/PhysRevE.62.3455 [13] DOI: 10.1063/1.1899283 · Zbl 1080.37106 [14] Krasovskii N., Stability of Motion (1963) [15] DOI: 10.1016/j.physa.2004.05.058 [16] DOI: 10.1109/TCSI.2004.835655 · Zbl 1374.94915 [17] DOI: 10.1016/S0375-9601(02)00538-8 · Zbl 0995.92004 [18] DOI: 10.1063/1.2089207 · Zbl 1144.37378 [19] Lü J., IEEE Trans. Autom. Contr. 50 pp 841– [20] DOI: 10.1016/j.physleta.2006.01.085 [21] DOI: 10.1016/j.nonrwa.2006.07.010 · Zbl 1125.34031 [22] DOI: 10.1109/TCSI.2004.838308 · Zbl 1371.34118 [23] DOI: 10.1109/81.222798 · Zbl 0800.92038 [24] DOI: 10.1103/PhysRevE.58.3067 [25] DOI: 10.1103/PhysRevE.57.R2507 [26] DOI: 10.1038/35065725 · Zbl 1370.90052 [27] DOI: 10.1016/j.physa.2005.10.047 [28] DOI: 10.1142/S0218127402004802 · Zbl 1044.37561 [29] DOI: 10.1038/30918 · Zbl 1368.05139 [30] Wu C., IEEE Trans. Circuits Syst.-I 42 pp 430– [31] Xu S., IEEE Trans. Circuits Syst.-II 52 pp 349– 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.