Multiple scroll wave chimera states
Multiple scroll wave chimera states
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多种滚动波嵌合体状态
DOI：
10.1140/epjst/e2017-70007-1
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Y. Maistrenko
中科院分区：
文献类型：
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作者：
V. Maistrenko;O. Sudakov;Oleksiy Osiv;Y. Maistrenko
我们报告了三维（3D）多头嵌合态的出现，这些嵌合态显示出共存相干和不相干的自组织时空模式的级联。我们证明，在系统参数的适当变化下，不相干嵌合域的数量可以加性增长，从而产生滚动波嵌合体的头加级联。该现象是针对放置在具有周期性边界条件的单位 3D 立方体中的 N3 个同相振荡器的 Kuramoto 模型得出的，参数是耦合半径 r 和相位滞后 α。为了获得多头嵌合体，我们执行所谓的“克隆程序”，如下：选择一个样本单头3D嵌合体状态，进行适当的尺度变换，并将它们的一定数量的副本放入单位立方体中。之后，在初始条件略有扰动的情况下开始数值模拟，并持续足够长的时间以确认或拒绝状态的存在和稳定性。通过这种方式，发现多个滚动波嵌合体，包括那些具有不连贯滚动、Hopf 链接和三叶结的嵌合体，允许这种多头再生。另一方面，没有螺旋旋转的多个 3D 嵌合体，如连贯和非连贯的球、管、十字和层，似乎不稳定，即使初始扰动是任意小的，也会很快被破坏。
We report the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that the number of incoherent chimera domains can grow additively under appropriate variations of the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for the Kuramoto model ofN3identical phase oscillators placed in the unit 3D cube with periodic boundary conditions, parameters being the coupling radiusrand phase lag α. To obtain the multiheaded chimeras, we perform the so-called ‘cloning procedure’ as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After that, start numerical simulations with slightly perturbed initial conditions and continue them for a sufficiently long time to confirm or reject the state existence and stability. In this way it is found, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoil knots admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable and are destroyed rather fast even for arbitrarily small initial perturbations.