Abstract
More than a decade ago, a surprising coexistence of synchronous and asynchronous behavior called the chimera state was discovered in networks of nonlocally coupled identical phase oscillators. In later years, chimeras were found to occur in a variety of theoretical and experimental studies of chemical and optical systems, as well as models of neuron dynamics. In this work, we study two coupled populations of pendulum-like elements represented by phase oscillators with a second derivative term multiplied by a mass parameter m and treat the first order derivative terms as dissipation with parameter ∊ > 0. We first present numerical evidence showing that chimeras do exist in this system for small mass values 0 < m ≪ 1. We then proceed to explain these states by reducing the coherent population to a single damped pendulum equation driven parametrically by oscillating averaged quantities related to the incoherent population.
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Bountis, T., Kanas, V.G., Hizanidis, J. et al. Chimera states in a two–population network of coupled pendulum–like elements. Eur. Phys. J. Spec. Top. 223, 721–728 (2014). https://doi.org/10.1140/epjst/e2014-02137-7
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DOI: https://doi.org/10.1140/epjst/e2014-02137-7