Synchronization patterns in networks of Kuramoto oscillators: A geometric approach for analysis and control
作者： Lorenzo Tiberi , Chiara Favaretto , Mario Innocenti , Danielle S. Bassett , Fabio Pasqualetti
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摘要: Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize formation synchronization patterns in networks Kuramoto oscillators. Specifically, reveal conditions on network weights, structure oscillators' frequencies that allow phases a group oscillators to evolve cohesively, yet independently from different clusters. Our are applicable general directed weighted heterogeneous Surprisingly, although exhibit nonlinear dynamics, our approach relies entirely tools linear algebra graph theory. Further, develop control mechanism determine smallest (as measured by Frobenius norm) perturbation ensure desired pattern. procedure allows us constrain set edges can be modified, thus enforcing sparsity perturbation. The results validated through numerical examples.
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sci-hub.se 参考文章(23)
Frank L. Lewis, Hongwei Zhang, Kristian Hengster-Movric, Abhijit Das, Introduction to Synchronization in Nature and Physics and Cooperative Control for Multi-Agent Systems on Graphs Communications and Control Engineering. pp. 1- 21 ,(2014) , 10.1007/978-1-4471-5574-4_1
Alfons Schnitzler, Joachim Gross, Normal and pathological oscillatory communication in the brain Nature Reviews Neuroscience. ,vol. 6, pp. 285- 296 ,(2005) , 10.1038/NRN1650
Klaus Lehnertz, Stephan Bialonski, Marie-Therese Horstmann, Dieter Krug, Alexander Rothkegel, Matthäus Staniek, Tobias Wagner, Synchronization phenomena in human epileptic brain networks. Journal of Neuroscience Methods. ,vol. 183, pp. 42- 48 ,(2009) , 10.1016/J.JNEUMETH.2009.05.015
Florian Dörfler, Francesco Bullo, Synchronization in complex networks of phase oscillators: A survey Automatica. ,vol. 50, pp. 1539- 1564 ,(2014) , 10.1016/J.AUTOMATICA.2014.04.012
Zhifei Zhang, Alain Sarlette, Zhihao Ling, Synchronization of kuramoto oscillators with non-identical natural frequencies: a quantum dynamical decoupling approach 53rd IEEE Conference on Decision and Control. pp. 4585- 4590 ,(2014) , 10.1109/CDC.2014.7040105
Judith Lehnert, Eckehard Schöll, Thomas Dahms, Cluster and group synchronization in delay-coupled networks. Physical Review E. ,vol. 86, pp. 016202- ,(2012) , 10.1103/PHYSREVE.86.016202
Louis M. Pecora, Francesco Sorrentino, Aaron M. Hagerstrom, Thomas E. Murphy, Rajarshi Roy, Cluster synchronization and isolated desynchronization in complex networks with symmetries Nature Communications. ,vol. 5, pp. 4079- ,(2014) , 10.1038/NCOMMS5079
Jeong-Rae Kim, Dongkwan Shin, Sung Hoon Jung, Pat Heslop-Harrison, Kwang-Hyun Cho, None, A design principle underlying the synchronization of oscillations in cellular systems Journal of Cell Science. ,vol. 123, pp. 537- 543 ,(2010) , 10.1242/JCS.060061
Miroslav Mirchev, Lasko Basnarkov, Fernando Corinto, Ljupco Kocarev, Cooperative Phenomena in Networks of Oscillators With Non-Identical Interactions and Dynamics IEEE Transactions on Circuits and Systems I: Regular Papers. ,vol. 61, pp. 811- 819 ,(2014) , 10.1109/TCSI.2013.2284185
Yoshiki Kuramoto, Self-entrainment of a population of coupled non-linear oscillators Mathematical Problems in Theoretical Physics. ,vol. 39, pp. 420- 422 ,(1975) , 10.1007/BFB0013365