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Nonlinearity of local dynamics promotes multi-chimeras

Omelchenko, Iryna; Zakharova, Anna; Hövel, Philipp; Siebert, Julien; Schöll, Eckehard

Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. We examine how the character of the individual elements influences chimera states by studying networks of nonlocally coupled Van der Pol oscillators. Varying the bifurcation parameter of the Van der Pol system, we can interpolate between regular sinusoidal and strongly nonlinear relaxation oscillations and demonstrate that more pronounced nonlinearity induces multi-chimera states with multiple incoherent domains. We show that the stability regimes for multi-chimera states and the mean phase velocity profiles of the oscillators change significantly as the nonlinearity becomes stronger. Furthermore, we reveal the influence of time delay on chimera patterns. The investigation of coupled oscillatory systems is an important research field bridging between nonlinear dynamics, network science, and statistical physics, with a variety of applications in physics, biology, and technology. The analysis and numerical simulation of large networks with complex coupling schemes continue to open up new unexpected dynamical scenarios. Chimera states are an example for such intriguing phenomena; they exhibit a hybrid structure combining coexisting domains of both coherent (synchronized) and incoherent (desynchronized) dynamics and were first reported for the well-known model of phase oscillators. In this paper, we investigate the influence of the local dynamics of the oscillators upon the resulting chimera patterns. Using the Van der Pol oscillator, which is a model allowing for a continuous transition between sinusoidal and strongly nonlinear relaxation oscillations by tuning a single parameter, we show that multi-chimera patterns with multiple incoherent domains are promoted by increasing the nonlinearity of the local oscillator dynamics
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.4927829, 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 25, 083104 (2015) and may be found at https://doi.org/10.1063/1.4927829.