Finding Non-Zero Stable Fixed Points of the Weighted Kuramoto model is NP-hard

Preprint English OPEN
Taylor, Richard;
  • Subject: Mathematical Physics

The Kuramoto model when considered over the full space of phase angles [$0,2\pi$) can have multiple stable fixed points which form basins of attraction in the solution space. In this paper we illustrate the fundamentally complex relationship between the network topology... View more
  • References (25)
    25 references, page 1 of 3

    [1] Acebron J A, Bonilla L L, Vicente C J P, Rotort F, and Spigler F 2005 The Kuramoto model: A simple paradigm for synchronization phenomena, Reviews of Modern Physics, 77, pp. 137-185.

    [2] Arenas A, Diaz-Guilera A, Kurths J, Moreno Y, and Zhou C 2008 Synchronization in complex networks, Phys. Rep., 469, pp. 93-153.

    [3] Bronski J C, DeVille L, and Park M J 2012 Fully synchronous solutions and the synchronization phase transition for the nite-N Kuramoto model, Chaos, 22, 033133.

    [4] Canale E A, Monzon P A, and Robledo F 2010 The Wheels: an In nite family of Bi-connected Planar Synchronizing Graphs, IEEE Conf. Industrial Electronics and Applications - Taichung, Tiawan, pp. 2202-2209.

    [5] Dekker A H 2010 Average distance as a predictor of synchronizability in networks of coupled oscillators, Proceedings of the 33rd Australian Computer Science Conference, CRPIT 102, Australian Computer Society, Canberra, Australia, pp. 127-131..

    [6] Dekker A H 2011 Analyzing C2 Structures and self-synchronization with simple computational models, Proceedings of the 16th ICCRTS, Quebec City, Canada.

    [7] Dekker A H, and Taylor R 2013 Synchronization properties of trees in the Kuramoto model, SIAM Journal on Applied Dynamical Systems, 12 (2), pp. 596-617.

    [8] Dor er F, and Bullo F 2013 Synchronization in Complex Networks: A Survey, Automatica, in review.

    [9] Dorogotsev S N, Goltsev A V, and Mendes J F F 2008 Critical phenomena in complex networks, Rev. Modern Phys., 80, pp. 1275-1353.

    [10] Garey M R, and Johnson D S 1979 Computers and Intractability - A guide to the theory of NP-Completeness, W H Freemean, New York.

  • Metrics
Share - Bookmark