WIAS Preprint No. 1213, (2007)

Destabilization patterns in large regular networks



Authors

  • Yanchuk, Serhiy
  • Wolfrum, Matthias

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt, 02.30.Oz, 89.75.Fb, 82.40.Ck

Keywords

  • Networks, coupled oscillators, bifurcations, Eckhaus instability

Abstract

We describe a generic mechanism for the destabilization in large regular networks of identical coupled oscillators. Based on a reduction method for the spectral problem, we first present a criterion for this type of destabilization. Then, we investigate the related bifurcation scenario, showing the existence of a large number of coexisting periodic solutions with different frequencies, spatial patterns, and stability properties. Even for unidirectional coupling this can be understood in analogy to the well-known Eckhaus scenario for diffusive systems.

Appeared in

  • Phys. Rev. E, 77 (2008) pp. 026212/1-026212/7.

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