Pimentel Jaime A, Aldana Maximino, Huepe Cristián, Larralde Hernán
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, Cuernavaca, Morelos, Mexico.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 1):061138. doi: 10.1103/PhysRevE.77.061138. Epub 2008 Jun 27.
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 [Phys. Rev. Lett. 75, 1226 (1995)] to describe the collective motion of groups of organisms. Two different types of noise, which we call intrinsic and extrinsic, are considered. The intrinsic noise, the one used by Vicsek 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 [Phys. Rev. Lett. 92, 025702 (2004)], affects the signal that the particles receive from the environment. The network models presented here can be considered as mean-field representations 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.
我们分析了由噪声驱动的有序-无序相变，这种相变发生在两种与维克塞克提出的自驱动模型密切相关的网络模型中[《物理评论快报》75, 1226 (1995)]，该模型用于描述生物群体的集体运动。我们考虑了两种不同类型的噪声，我们称之为内在噪声和外在噪声。内在噪声是维克塞克在其原始工作中使用的那种，它与粒子更新其位置的决策机制有关。相比之下，外在噪声是后来由格雷瓜尔和沙泰[《物理评论快报》92, 025702 (2004)]引入的，它影响粒子从环境中接收到的信号。这里提出的网络模型可以被视为自驱动模型的平均场表示。我们通过解析和数值方法表明，对于这两种网络模型，由内在噪声驱动的相变是连续的，而外在噪声会产生不连续的相变。即使对于小世界拓扑结构也是如此，它会在网络元素之间诱导出很强的空间相关性。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，相变可以是连续的或不连续的，这取决于每种类型噪声的幅度。
