Cheng, Chang-Yuan Induction of Hopf bifurcation and oscillation death by delays in coupled networks. (English) Zbl 1235.34090 Phys. Lett., A 374, No. 2, 178-185 (2009). Summary: This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay. Cited in 10 Documents MSC: 34B45 Boundary value problems on graphs and networks for ordinary differential equations 34K18 Bifurcation theory of functional-differential equations 34K20 Stability theory of functional-differential equations Keywords:networks; bifurcation; delay equations PDFBibTeX XMLCite \textit{C.-Y. Cheng}, Phys. Lett., A 374, No. 2, 178--185 (2009; Zbl 1235.34090) Full Text: DOI References: [1] Atay, F. M., J. Differential Equations, 221, 190 (2006) · Zbl 1099.34066 [2] Dias, A. P.S.; Lamb, J. S.W., Physica D, 223, 93 (2006) [3] Drubi, F.; Ibáñez, S.; Rodríguez, J. A., J. Differential Equations, 239, 371 (2007) [4] Peng, Y.; Song, Y., Phys. Lett. A, 373, 1744 (2009) [5] Zhang, C.; Zhang, Y.; Zheng, B., J. Comp. Appl. Math., 229, 264 (2009) [6] Li, C.; Xu, C.; Sun, W.; Xu, J.; Kurths, J., Chaos, 393, 013106 (2009) [7] Guo, S.; Huang, L., Physica D, 183, 19 (2003) [8] Campbell, S. A.; Yuan, Y.; Bungay, S. B., Nonlinearity, 18, 2827 (2005) [9] Watts, D. J.; Strogatz, S. H., Nature, 393, 440 (1998) [10] Xu, X.; Wang, Z. H., Nonlinear Dyn., 56, 127 (2009) [11] McCann, K.; Hastings, A.; Huxel, G. R., Nature, 395, 794 (1998) [12] Berlow, E. L., Nature, 398, 330 (1999) [13] Li, C.; Sun, W.; Kurths, J., Phys. Rev. E, 76, 046204 (2007) [14] Campbell, S. A.; Edwards, R.; Van Den Driessche, P., SIAM J. Appl. Math., 65, 316 (2004) [15] Hale, J.; Lunel, S. M.V., Introduction to Functional Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002 [16] Hu, H. Y.; Wang, Z. H., Dynamics of Controlled Mechanical Systems with Delayed Feedback (2002), Springer: Springer Heidelberg [17] Hassard, B. D.; Kazarinoff, N. D.; Wan, Y. H., Theory and Application of Hopf Bifurcation (1981), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0474.34002 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.