Wolfrum Matthias, Omel'chenko Oleh E
Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):015201. doi: 10.1103/PhysRevE.84.015201. Epub 2011 Jul 8.
Spatiotemporal chaos and turbulence are universal concepts for the explanation of irregular behavior in various physical systems. Recently, a remarkable new phenomenon, called "chimera states," has been described, where in a spatially homogeneous system, regions of irregular incoherent motion coexist with regular synchronized motion, forming a self-organized pattern in a population of nonlocally coupled oscillators. Whereas most previous studies of chimera states focused their attention on the case of large numbers of oscillators employing the thermodynamic limit of infinitely many oscillators, here we investigate the properties of chimera states in populations of finite size using concepts from deterministic chaos. Our calculations of the Lyapunov spectrum show that the incoherent motion, which is described in the thermodynamic limit as a stationary behavior, in finite size systems appears as weak spatially extensive chaos. Moreover, for sufficiently small populations the chimera states reveal their transient nature: after a certain time span we observe a sudden collapse of the chimera pattern and a transition to the completely coherent state. Our results indicate that chimera states can be considered as chaotic transients, showing the same properties as type-II supertransients in coupled map lattices.
时空混沌和湍流是用于解释各种物理系统中不规则行为的通用概念。最近，一种被称为“奇异态”的显著新现象被描述出来，即在空间均匀的系统中，不规则非相干运动区域与规则同步运动共存，在一群非局部耦合振子中形成一种自组织模式。尽管之前关于奇异态的大多数研究都将注意力集中在采用无限多个振子的热力学极限的大量振子的情况上，但在这里我们使用确定性混沌的概念来研究有限规模群体中奇异态的性质。我们对李雅普诺夫谱的计算表明，在热力学极限中被描述为平稳行为的非相干运动，在有限规模系统中表现为微弱的空间扩展混沌。此外，对于足够小的群体，奇异态显示出它们的瞬态性质：在一定时间跨度后，我们观察到奇异模式突然崩溃并转变为完全相干态。我们的结果表明，奇异态可被视为混沌瞬态，表现出与耦合映射格中的II型超瞬态相同的性质。
