Bonciolini Giacomo, Ebi Dominik, Boujo Edouard, Noiray Nicolas
CAPS Laboratory, MAVT department ETH Zürich, Sonneggstrasse 3, 8092, Zurich, Switzerland.
Laboratory for Thermal Processes and Combustion, Paul Scherrer Institute, 5232 Villigen, Switzerland.
R Soc Open Sci. 2018 Mar 21;5(3):172078. doi: 10.1098/rsos.172078. eCollection 2018 Mar.
Complex systems exhibiting critical transitions when one of their governing parameters varies are ubiquitous in nature and in engineering applications. Despite a vast literature focusing on this topic, there are few studies dealing with the effect of the rate of change of the bifurcation parameter on the tipping points. In this work, we consider a subcritical stochastic Hopf bifurcation under two scenarios: the bifurcation parameter is first changed in a quasi-steady manner and then, with a finite ramping rate. In the latter case, a rate-dependent bifurcation delay is observed and exemplified experimentally using a thermoacoustic instability in a combustion chamber. This delay increases with the rate of change. This leads to a state transition of larger amplitude compared with the one that would be experienced by the system with a quasi-steady change of the parameter. We also bring experimental evidence of a dynamic hysteresis caused by the bifurcation delay when the parameter is ramped back. A surrogate model is derived in order to predict the statistic of these delays and to scrutinize the underlying stochastic dynamics. Our study highlights the dramatic influence of a finite rate of change of bifurcation parameters upon tipping points, and it pinpoints the crucial need of considering this effect when investigating critical transitions.
当控制参数之一发生变化时，呈现临界转变的复杂系统在自然界和工程应用中普遍存在。尽管有大量文献关注这一主题，但很少有研究探讨分岔参数变化率对临界点的影响。在这项工作中，我们考虑了两种情况下的亚临界随机霍普夫分岔：分岔参数首先以准稳态方式变化，然后以有限的斜率变化。在后一种情况下，观察到了与速率相关的分岔延迟，并通过燃烧室中的热声不稳定性进行了实验验证。这种延迟随着变化率的增加而增大。这导致与参数准稳态变化的系统相比，出现更大幅度的状态转变。当参数反向斜坡变化时，我们还给出了由分岔延迟引起的动态滞后的实验证据。为了预测这些延迟的统计数据并仔细研究潜在的随机动力学，我们推导了一个替代模型。我们的研究突出了分岔参数有限变化率对临界点的巨大影响，并指出在研究临界转变时考虑这种影响的迫切需求。
