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APS » Journals » Phys. Rev. Lett. » Volume 93 » Issue 11
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Phys. Rev. Lett. 93, 114101 (2004) [4 pages]

Desynchronization Waves and Localized Instabilities in Oscillator Arrays

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Juan G. Restrepo1,2,*, Edward Ott1,3, and Brian R. Hunt2,4
1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
2Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
3Department of Physics and Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA
4Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA

Received 7 April 2004; published 7 September 2004

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.93.114101
DOI:
10.1103/PhysRevLett.93.114101
PACS:
05.45.Xt, 89.75.–k

*Electronic address: juanga@math.umd.edu

 
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