Gopalakrishnan E A, Sharma Yogita, John Tony, Dutta Partha Sharathi, Sujith R I
Department of Aerospace Engineering, Indian Institute of Technology Madras, 600036, India.
Department of Mathematics, Indian Institute of Technology Ropar, 140001, India.
Sci Rep. 2016 Oct 21;6:35310. doi: 10.1038/srep35310.
Dynamical systems can undergo critical transitions where the system suddenly shifts from one stable state to another at a critical threshold called the tipping point. The decrease in recovery rate to equilibrium (critical slowing down) as the system approaches the tipping point can be used to identify the proximity to a critical transition. Several measures have been adopted to provide early indications of critical transitions that happen in a variety of complex systems. In this study, we use early warning indicators to predict subcritical Hopf bifurcation occurring in a thermoacoustic system by analyzing the observables from experiments and from a theoretical model. We find that the early warning measures perform as robust indicators in the presence and absence of external noise. Thus, we illustrate the applicability of these indicators in an engineering system depicting critical transitions.
动力系统可能会经历临界转变，即系统在一个被称为临界点的临界阈值处突然从一种稳定状态转变为另一种稳定状态。当系统接近临界点时，恢复到平衡态的速率下降（临界减慢）可用于识别接近临界转变的程度。已经采用了几种方法来提供各种复杂系统中发生的临界转变的早期迹象。在本研究中，我们通过分析实验和理论模型中的可观测量，使用早期预警指标来预测热声系统中发生的亚临界霍普夫分岔。我们发现，无论有无外部噪声，早期预警指标都能作为稳健的指标发挥作用。因此，我们说明了这些指标在描述临界转变的工程系统中的适用性。
