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Chimera states and the interplay between initial conditions and non-local coupling

Kalle, Peter; Sawicki, Jakub; Zakharova, Anna; Schöll, Eckehard

Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We study chimera states in a network of non-locally coupled Stuart-Landau oscillators. We investigate the impact of initial conditions in combination with non-local coupling. Based on an analytical argument, we show how the coupling phase and the coupling strength are linked to the occurrence of chimera states, flipped profiles of the mean phase velocity, and the transition from a phase- to an amplitude-mediated chimera state. Chimera states are an example of intriguing partial synchronization patterns appearing in networks of identical oscillators with symmetric coupling scheme. They exhibit a hybrid structure combining coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics and were first reported for the model of phase oscillators. Recent studies have demonstrated the emergence of chimera states in a variety of topologies and for different types of individual dynamics. In this paper, the interplay between initial conditions and non-local coupling is studied. We show that, based on an analytical argument incorporating the initial conditions and the range of non-local coupling, the occurrence of phase chimeras can be seen as caused by a phase lag in the coupling. Considering the dynamics of chimera states, our argument shows how “flipped” profiles of the mean phase velocities can be explained by a change of sign of the coupling phase. By this, one can either choose a concave (“upside”) profile of the mean phase velocities or a “flipped” one. Extending our reasoning, we show that this argument intuitively explains the transition from a phase- to an amplitude-mediated chimera state as a result of increasing coupling strength.
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.4977866, American Institute of Physics (AIP)
  • This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 27, 033110 (2017) and may be found at https://doi.org/10.1063/1.4977866.