Quasiperiodic and chaotic discrete breathers in a parametrically driven system without linear dispersion.
Quasiperiodic and chaotic discrete breathers in a parametrically driven system without linear dispersion.
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无线性色散的参数驱动系统中的准周期和混沌离散呼吸器。
DOI：
10.1103/physreve.73.046211
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
T. Bountis
中科院分区：
文献类型：
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作者：
P. Maniadis;T. Bountis
我们研究一个一维晶格的非谐振子只有四次最近邻相互作用，其中离散呼吸子（DB的）可以明确地构建一个精确的分离，他们的时间和空间的依赖性。引入参数周期驱动，我们首先展示了如何各种这样的DB的可以通过选择空间配置文件从同宿轨道的可逆映射，并将它们与初始条件从庞加莱表面的一个简单的Duffing方程的部分选择。然后将我们的初始条件放置在主要共振的岛屿的中心，我们演示了如何通过改变驱动的振幅来稳定相应的DB。因此，我们发现椭圆点周围的一个大区域的准周期呼吸子，这是稳定的很长一段时间。从接近原点椭圆点的初始条件出发，我们发现当我们接近主混沌层时，准周期呼吸子要么通过离域化而失稳，要么在崩溃前变成具有明显宽带傅立叶谱的混沌呼吸子.对于一些呼吸器配置文件稳定的准周期呼吸器存在的所有方式的分界线的Duffing方程，表明在多维相空间中的DB解决方案周围的大区域的环面的存在。我们认为，这些强烈的本地化现象是由于声子共振的情况下，没有线性色散项在我们的晶格。然而，我们还表明，这些现象持续存在于更现实的物理模型，其中弱线性色散包括在运动方程中，具有足够小的系数。
We study a one-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DB's) can be explicitly constructed by an exact separation of their time and space dependence. Introducing parametric periodic driving, we first show how a variety of such DB's can be obtained by selecting spatial profiles from the homoclinic orbits of an invertible map and combining them with initial conditions chosen from the Poincaré surface of section of a simple Duffing's equation. Placing then our initial conditions at the center of the islands of a major resonance, we demonstrate how the corresponding DB can be stabilized by varying the amplitude of the driving. We thus discover around elliptic points a large region of quasiperiodic breathers, which are stable for very long times. Starting with initial conditions close to the elliptic point at the origin, we find that as we approach the main chaotic layer, a quasiperiodic breather either destabilizes by delocalization or turns into a chaotic breather, with an evidently broadbanded Fourier spectrum before it collapses. For some breather profiles stable quasiperiodic breathers exist all the way to the separatrix of the Duffing equation, indicating the presence of large regions of tori around the DB solution in the multidimensional phase space. We argue that these strong localization phenomena are due to the absence of phonon resonances, as there are no linear dispersion terms in our lattices. We also show, however, that these phenomena persist in more realistic physical models, in which weak linear dispersion is included in the equations of motion, with a sufficiently small coefficient.