New PDF release: Chaos ~ An Interdisciplinary Journal of Nonlinear Science ~

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Additional resources for Chaos ~ An Interdisciplinary Journal of Nonlinear Science ~ March 2009 Volume 19, Issue 1

Example text

In unweighted networks, Wij = 1 is uniform for all the incoming links. In the original DO mechanism,20 we increase the coupling strength of only one incoming link of oscillator i by a small value, at the time step tn = t0 + n␶, where n ജ 1 is the positive integer, t0 is the transient time, and ␶ Ͼ 0 is the duration time. This adaptation results from the competition between neighbor oscillators within the interval ͓tn−1 , tn͒. , En͑i , j͒ = ͐ttn ␾͑xi , x j͒dt, within the interval n−1 ͓tn−1 , tn͒ is evaluated, where ␾ is a non-negative error function, and satisfies ␾͑xi , x j͒ = 0 if oscillators i , j are synchro- nized.

64, 821 ͑1990͒. T. L. Caroll and L. M. Pecora, IEEE Trans. Circuits Syst. 38, 453 ͑1991͒. 3 A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences ͑Cambridge University Press, Cambridge, 2003͒. 4 N. F. Rulkov and M. M. Sushchik, Phys. Rev. E 51, 980 ͑1995͒. 5 M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 ͑1997͒. 6 M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 ͑1996͒. 7 Q. Jia, Phys. Lett. A 370, 40 ͑2007͒.

5͒ is n0 = 1200. 001. From Fig. 1, the synchronization in network ͑1͒ is realized effectively. From Eqs. ͑2͒ and ͑5͒, all the oscillators have uniform intensities during the transition to synchronization, regardless of heterogeneous degrees and initial conditions. 8 ͑Fig. 2͒. 11 From Eqs. ͑2͒ and ͑5͒, the incoming link to be adjusted for each oscillator is always chosen to be the pair of oscillators with the maximal synchronization difference in the previous time interval, which greatly decrease the ratio Re͑␭N͒ / Re͑␭2͒.

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