WIAS Preprint No. 2069, (2015)

Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators



Authors

  • Wolfrum, Matthias
  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878
  • Sieber, Jan

2010 Mathematics Subject Classification

  • 34C15 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 89.75.Kd

Keywords

  • Coupled oscillators, regular and irregular patterns, self-localized excitation, chimera states, route to chaos

Abstract

We study a system of phase oscillators with non-local coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.

Appeared in

  • Chaos, 25 (2015) pp. 053113/1--053113/7.

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