Phase-dependent output of scattering process for traveling breathers.
Phase-dependent output of scattering process for traveling breathers.
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旅行呼吸者散射过程的相位相关输出。
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Y. Nishiura
中科院分区：
文献类型：
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作者：
T. Teramoto;Kei;Y. Nishiura
研究了具有外力的复Ginzburg-Landau方程(CGLE)和激活剂-基质-抑制剂三组分模型的一维行进呼吸子(TBS)之间的散射过程，即振荡行波脉冲.一般情况下，输入-输出关系依赖于两个TBS在碰撞点的相位，这与稳定行波脉冲的情况形成了对比。一个被称为散射体的隐藏的不稳定解对于理解散射动力学起着至关重要的作用。散射体的稳定流形和不稳定流形直接决定着散布过程中的交通流。参数空间中输入输出关系的一个过渡点，如从保存到湮灭，对应于轨道穿过散射体的稳定流形时。输入输出关系的位相依赖来自于这样一个事实，即在碰撞点处的轮廓使环路由位相参数化，并遍历散射体的稳定流形。全局分叉的观点不仅对于理解TBS是如何出现的，而且对于探测散射体都是非常有用的。结果表明，CGLE(分别为三组分系统)的散射体变成了一个不稳定的时间周期(分别为定常)解。
Scattering process between one-dimensional traveling breathers (TBs), i.e., oscillatory traveling pulses, for the complex Ginzburg-Landau equation (CGLE) with external forcing and a three-component activator-substrate-inhibitor model are studied. The input-output relation depends in general on the phase of two TBs at collision point, which makes a contrast to the case for the steady traveling pulses. A hidden unstable solution called the scattor plays a crucial role to understand the scattering dynamics. Stable and unstable manifolds of the scattor direct the traffic flows of the scattering process. A transition point of the input-output relation in a parameter space such as from preservation to annihilation corresponds to when the orbit crosses the stable manifold of the scattor. The phase dependency of input-output relation comes from the fact that the profiles at collision point make a loop parametrized by the phase and it traverses the stable manifold of the scattor. A global bifurcation viewpoint is quite useful not only to understand how TBs emerge but also to detect scattors. It turns out that the scattor for the CGLE (respectively the three-component system) becomes an unstable time-periodic (respectively stationary) solution.