%0 Journal Article %1 citeulike:1189179 %A Park, K. %A Huang, L. %A Lai, Y. C. %C Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA. %D 2007 %J Phys Rev E Stat Nonlin Soft Matter Phys %K no-tag %N 2 Pt 2 %T Desynchronization waves in small-world networks. %U http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=17358409 %V 75 %X A regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased, due to the spread of localized instability of eigenvectors of the Laplacian matrix. We find that shortcuts, which make a regular network small-world, can destroy ordered desynchronization wave patterns. Wave patterns in a small-world network are usually destroyed gradually as the degree of regularity in the network deteriorates. No ordered wave patterns are observed in scale-free and random networks. The formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator. We derive a general type of the Kardar-Parisi-Zhang equation for phase evolution in a prototype oscillator network. The equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts. Our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise.

@article{citeulike:1189179, abstract = {A regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased, due to the spread of localized instability of eigenvectors of the Laplacian matrix. We find that shortcuts, which make a regular network small-world, can destroy ordered desynchronization wave patterns. Wave patterns in a small-world network are usually destroyed gradually as the degree of regularity in the network deteriorates. No ordered wave patterns are observed in scale-free and random networks. The formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator. We derive a general type of the Kardar-Parisi-Zhang equation for phase evolution in a prototype oscillator network. The equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts. Our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise.}, added-at = {2007-08-18T13:22:24.000+0200}, address = {Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287, USA.}, author = {Park, K. and Huang, L. and Lai, Y. C.}, biburl = {https://www.bibsonomy.org/bibtex/243a341abfd04079bb05beb37d7b2f3cd/a_olympia}, citeulike-article-id = {1189179}, description = {citeulike}, interhash = {43b164ab60c6da134a16abd224d28459}, intrahash = {43a341abfd04079bb05beb37d7b2f3cd}, issn = {1539-3755}, journal = {Phys Rev E Stat Nonlin Soft Matter Phys}, keywords = {no-tag}, month = {February}, number = {2 Pt 2}, priority = {2}, timestamp = {2007-08-18T13:22:30.000+0200}, title = {Desynchronization waves in small-world networks.}, url = {http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve\&db=pubmed\&dopt=Abstract\&list_uids=17358409}, volume = 75, year = 2007 }