Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators
Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators
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DOI：
10.1088/0951-7715/10/3/006
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发表时间：
1997-05
期刊：
影响因子：
1.7
通讯作者：
J. Sepulchre;R. MacKay
中科院分区：
文献类型：
--
作者：
J. Sepulchre;R. MacKay
我们解决的问题，在耦合网络的空间局部化周期振荡-所谓的离散呼吸-在一般情况下。这方面是有关的一般条件，允许连续的向量场的周期解。我们的方法的一个优点是在同一个数学框架中包含保守和耗散系统的情况。一个基本特征是我们允许周期变化。特别是，我们推导出存在的离散呼吸网络中的每个网站有一个平衡和一些网站有一个极限环，并在哈密顿网络，而不需要当地的非谐性。后一种情况下处理考虑持久性的家庭的周期性解决方案在更广泛的背景下，系统的积分，而不仅仅是哈密顿的。
We address the issue of spatially localized periodic oscillations in coupled networks - so-called discrete breathers - in a general context. This context is concerned with general conditions which allow continuation of periodic solutions of vector fields. One advantage of our approach is to encompass in the same mathematical framework the cases of conservative and dissipative systems. An essential feature is that we allow the period to vary. In particular, we deduce existence of discrete breathers in networks where each site has an equilibrium and some sites have a limit cycle, and in Hamiltonian networks without requiring local anharmonicity. The latter case is dealt with by considering the persistence of families of periodic solutions in the more general context of systems with an integral, not just Hamiltonian ones.