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Induction of Hopf bifurcation and oscillation death by delays in coupled networks. (English) Zbl 1235.34090

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.

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
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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
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