多重涡卷波嵌合态
Multiple scroll wave chimera states
摘要：
我们指的是三维（3D）多头嵌合体状态，显示级联的自组织的时空模式共存的一致性和不一致性的外观。我们证明了在适当改变系统参数的情况下，非相干嵌合体的畴数可以相加地增长，从而产生涡卷波嵌合体的头相加级联。本文推导了仓本模型中N个同相振子在周期性边界条件下的耦合半径$r$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，并将它们的一些副本放入单位立方体。然后，在足够长的时间内以轻微扰动的初始条件开始数值模拟，以确认或否认状态的存在性和稳定性。它被发现，通过这种方式，多个涡卷波嵌合体，包括那些不连贯的轧辊，霍普夫链接和三叶承认这种多头再生。另一方面，没有螺旋旋转的多个3D嵌合体，如连贯和不连贯的球、管、十字架和层，即使有任何小的扰动，也会很快被破坏。
英文摘要：
We refer 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 number of the incoherent chimera's domains can grow additively under appropriate varying the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for Kuramoto model of N identical phase oscillators placed in the 3D cube with periodic boundary conditions, parameters are coupling radius $r$ and 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, start numerical simulations with slightly perturbed initial conditions for long enough time to confirms or denies the state existence and stability. It is found, by this a way, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoils 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 under are destroyed rather fast even with any small perturbations.
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