page_title: Kuramoto model
section_title: Variations of the models
hierarchical_section_title: Kuramoto model / Variations of the models
caption_attribution_description: English: Shows four distinct synchronization patterns in a 128x128 array of Kuramoto-like oscillators with differing phase interaction functions and spatial coupling topologies. (A) Pinwheels arise from sinuoidal phase interactions combined with Gaussian spatial coupling. (B) Waves arise from sinusoidal phase interactions combined with Mexican-Hat spatial coupling. (C) Chimeras arise with the introduction of second Fourier component in the phase interaction, in this case combined with Gaussian spatial coupling. (D) Chimeras and waves arise from a second-order phase interaction combined with Mexican-Hat spatial coupling. See Kuramoto Model.
context_page_description: The Kuramoto model, first proposed by Yoshiki Kuramoto, is a mathematical model used to describe synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the behavior of systems of chemical and biological oscillators, and it has found widespread applications such as in neuroscience and oscillating flame dynamics. Kuramoto was quite surprised when the behavior of some physical systems, namely coupled arrays of Josephson junctions, followed his model.
  The model makes several assumptions, including that there is weak coupling, that the oscillators are identical or nearly identical, and that interactions depend sinusoidally on the phase difference between each pair of objects.
context_section_description: There are a number of types of variations that can be applied to the original model presented above. Some models change to topological structure, others allow for heterogeneous weights, and other changes are more related to models that are inspired by the Kuramoto model but do not have the same functional form.
caption: Distinct synchronization patterns in a two-dimensional array of Kuramoto-like oscillators with differing phase interaction functions and spatial coupling topologies.  (A) Pinwheels. (B) Waves. (C) Chimeras. (D) Chimeras and waves combined. Color scale indicates oscillator phase.
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