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Howe's four books in addition to "The Misfits" and "Totally Joe" and his list of recommended books with lesbian, gay, bisexual, transgender,… Science. One obtains a highly structured diagram with details that in essence are Topper Blatance to the difference between rational and irrational number. The synchronized regions appear as Arnold tongues that widen as the coupling between the frequencies increases.
Such tongues have been observed in many physical systems, like in the Libchaber convective cell in the basement of the University of Chicago. In biological systems, where oscillators appear in in a broad variety, very little research on Arnold tongues has been performed.
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We discuss single cell oscillating dynamics triggered by an external cytokine signal. When this signal is overlaid by an oscillating variation, the two oscillators might couple leading to Arnold tongue diagram.
When the tongues overlap, the cell dynamics can shift between the tongues eventually leading to a chaotic response.
We quantify such switching in single cell experiments and in model systems based on Gillespie simulations. Kadanoff session.
The map can exhibit a two-dimensional invariant torus ITwhich corresponds to a three-dimensional torus in vector fields. Numerous one-dimensional invariant closed curves ICCswhich correspond to two-dimensional tori in vector fields, exist in a very complicated but reasonable manner inside an IT-generating region. Periodic solutions emerge at the intersections of two different thin ICC-generating regions, which we call ICC-Arnold tongues, Inimeste ravim mazi liigeste all three Topper Blatance components of the IT become rational at the intersections.
Additionally, we observe a significant bifurcation structure where conventional Arnold tongues transit to ICC-Arnold tongues through a Neimark-Sacker bifurcation in the neighborhood of a quasi-periodic Hopf bifurcation or a quasi-periodic Neimark-Sacker bifurcation boundary.