Synchronization of frequency-weighted coupled complex systems driven by leader
Received date: 2018-03-26
Online published: 2018-12-23
金彦亮, 朱怀清, 齐崎, 周润滋 . 领导者驱动下频率权重耦合复杂系统的同步[J]. 上海大学学报(自然科学版), 2020 , 26(3) : 393 -400 . DOI: 10.12066/j.issn.1007-2861.2047
The complex systems which consist of a large number of coupled oscillators are widely present in the real world. Complex systems not only form spontaneous synchronization through coupling, but also often suffer from external influences and exhibit complex dynamic behavior. This paper studies the important collective dynamic behavior known as systems synchronization when the oscillators are driven by an external leader node. It lays out the conditions under which the frequency-weighted coupled system consisting of Kuramoto oscillators becomes synchronized when the system is driven by an external leader. The number and the frequency-weight of the driven oscillators affect the ease of the system transitions to driven synchronization. The simulation result shows that the results obtained are correct.
Key words： complex system; external drive; synchronization
| [1] | D?rfler F, Bullo F. Synchronization in complex networks of phase oscillators: a survey[J]. Automatica, 2014,50(6):1539-1564. |
| [2] | Anderson P W. The economy as an evolving complex system [M]. Boca Raton: CRC Press, 2018. |
| [3] | Zhang F, Liao X, Zhang G. Some new results for the generalized lorenz system[J]. Qualitative Theory of Dynamical Systems, 2016,16(3):1-11. |
| [4] | Dietert H. Stability and bifurcation for the Kuramoto model[J]. Journal De Mathématiques Pures Et Appliquées, 2016,105(4):451-489. |
| [5] | Do?fler F, Bullo F. Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators[C]// IEEE American Control Conference. 2010: 930-937. |
| [6] | Wang H, Li X. Bifurcations in a frequency-weighted Kuramoto oscillators network[J]. International Journal of Bifurcation and Chaos, 2012,22(9):1250230. |
| [7] | Liu Y L, Yu X M, Hao Y H. Analytical results for frequency-weighted Kuramoto-oscillator networks[J]. Chinese Physics Letters, 2015,32(11):110503. |
| [8] | Zhang X, Hu X, Kurths J, et al. Explosive synchronization in a general complex network[J]. Physical Review E, 2013,88(1):010802. |
| [9] | Xu C, Gao J, Xiang H, et al. Dynamics of phase oscillators in the Kuramoto model with generalized frequency-weighted coupling[J]. Physical Review E, 2016,94:062204 |
| [10] | Bi H J, Li Y, Zhou L, et al. Nontrivial standing wave state in frequency-weighted Kuramoto model[J]. Frontiers of Physics, 2017,12(3):126801. |
| [11] | Papo D, Buldú J M, Boccaletti S, et al. Complex network theory and the brain[J]. Philosophical Transactions of the Royal Society B, 2014,369:20130520. |
| [12] | Wang Y, Doyle F J. Exponential synchronization rate of Kuramoto oscillators in the presence of a pacemaker[J]. IEEE Transactions on Automatic Control, 2013,58(4):989-994. |
| [13] | Zou Y Y, Li H H. Paths to synchronization on complex networks with external drive[J]. Chinese Physics Letters, 2014,31(10):10-13. |
| [14] | Yuniati A, Mai T L, Chen C M. Noise-driven synchronization of coupled neural networks[J]. Biophysical Journal, 2016,110(3):631-632. |
| [15] | Seshadri A, Sujith R I. A bifurcation giving birth to order in an impulsively driven complex system[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016,26(8):083103. |
/
| 〈 |
|
〉 |
