具有交叉扩散的振动系统中的自发周期行波
Spontaneous periodic travelling waves in oscillatory systems with cross-diffusion
摘要：
我们确定了一种新类型的斑图形成在空间分布的主动系统。我们模拟了具有捕食者-食饵局部相互作用的一维两组分系统，组分之间具有追逐-逃避趋药性。在一个足够大的区域，空间均匀振荡在这样的系统是不稳定的小扰动。这种不稳定性，通过一个瞬态政权出现自发的焦点来源，导致建立周期性的行波。即使边界条件不支持这种解，也建立了行波状态。稳定的波长是在一个范围内界定的从上方和从下方，这个范围不符合不稳定带的空间均匀振荡。
英文摘要：
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently large domain, spatially uniform oscillations in such systems are unstable with respect to small perturbations. This instability, through a transient regime appearing as spontanous focal sources, leads to establishment of periodic traveling waves. The traveling waves regime is established even if boundary conditions do not favor such solutions. The stable wavelength are within a range bounded both from above and from below, and this range does not coincide with instability bands of the spatially uniform oscillations.
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