کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8256259 | 1533953 | 2018 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Synchronisation under shocks: The Lévy Kuramoto model
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Synchronisation under shocks: The Lévy Kuramoto model Synchronisation under shocks: The Lévy Kuramoto model](/preview/png/8256259.png)
چکیده انگلیسی
We study the Kuramoto model of identical oscillators on ErdÅs-Rényi (ER) and Barabasi-Alberts (BA) scale free networks examining the dynamics when perturbed by a Lévy noise. Lévy noise exhibits heavier tails than Gaussian while allowing for their tempering in a controlled manner. This allows us to understand how 'shocks' influence individual oscillator and collective system behaviour of a paradigmatic complex system. Skewed α-stable Lévy noise, equivalent to fractional diffusion perturbations, are considered, but overlaid by exponential tempering of rate λ. In an earlier paper we found that synchrony takes a variety of forms for identical Kuramoto oscillators subject to stable Lévy noise, not seen for the Gaussian case, and changing with α: a noise-induced drift, a smooth α dependence of the point of cross-over of synchronisation point of ER and BA networks, and a severe loss of synchronisation at low values of α. In the presence of tempering we observe both analytically and numerically a dramatic change to the α<1 behaviour where synchronisation is sustained over a larger range of values of the 'noise strength' Ï, improved compared to the α>1 tempered cases. Analytically we study the system close to the phase synchronised fixed point and solve the tempered fractional Fokker-Planck equation. There we observe that densities show stronger support in the basin of attraction at low α for fixed coupling, Ï and tempering λ. We then perform numerical simulations for networks of size N=1000 and average degree dÌ=10. There, we compute the order parameter r as a function of Ï for fixed α and λ and observe values of râ1 over larger ranges of Ï for α<1 and λâ 0. In addition we observe drift of both positive and negative slopes for different α and λ when native frequencies are equal, and confirm a sustainment of synchronisation down to low values of α. We propose a mechanism for this in terms of the basic shape of the tempered stable Lévy densities for various α and how it feeds into Kuramoto oscillator dynamics and illustrate this with examples of specific paths.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 368, 1 April 2018, Pages 10-21
Journal: Physica D: Nonlinear Phenomena - Volume 368, 1 April 2018, Pages 10-21
نویسندگان
Dale Roberts, Alexander C. Kalloniatis,