内、外噪声对群集系统相变的影响及相关网络模型
Intrinsic and extrinsic noise effects on the phase transition of swarming systems and related network models
摘要：
我们分析了由噪声驱动的有序-无序相变发生在两种网络模型密切相关的自推进模型Vicsek等。[ \emph{Phys. Rev. Lett.} { \bf 75}：1226（1995）]。两种不同类型的噪声，我们称之为内在和外在的，被认为是。固有噪声，Vicsek等人使用的一个。在他们的原始工作中，与粒子更新其位置的决策机制有关。相反，后来由Grégoire和Chaté [ \emph{Phys. Rev. Lett.} { \bf 92}：025702（2004）]引入的外部噪声影响颗粒从环境接收的信号。这里提出的网络模型可以被认为是自推进模型的平均场表示。我们分析和数值计算表明，对于这两个网络模型，由固有噪声驱动的相变是连续的，而外部噪声产生不连续的相变。即使对于小世界拓扑也是如此，它在网络元素之间引起了强烈的空间相关性。我们还分析了两种类型的噪声同时存在的情况。在这种情况下，取决于每种噪声的幅度，相变可以是连续的或不连续的。
英文摘要：
We analyze order-disorder phase transitions driven by noise that occur in two kinds of network models closely related to the self-propelled model proposed by Vicsek et. al. to describe the collective motion of groups of organisms [\emph{Phys. Rev. Lett.} {\bf 75}:1226 (1995)]. Two different types of noise, which we call intrinsic and extrinsic, are considered. The intrinsic noise, the one used by Vicsek et. al. in their original work, is related to the decision mechanism through which the particles update their positions. In contrast, the extrinsic noise, later introduced by Grégoire and Chaté [\emph{Phys. Rev. Lett.} {\bf 92}:025702 (2004)], affects the signal that the particles receive from the environment. The network models presented here can be considered as the mean-field representation of the self-propelled model. We show analytically and numerically that, for these two network models, the phase transitions driven by the intrinsic noise are continuous, whereas the extrinsic noise produces discontinuous phase transitions. This is true even for the small-world topology, which induces strong spatial correlations between the network elements. We also analyze the case where both types of noise are present simultaneously. In this situation, the phase transition can be continuous or discontinuous depending upon the amplitude of each type of noise.
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