Lee Minwoo, Guan Yu, Gupta Vikrant, Li Larry K B
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, China.
Phys Rev E. 2020 Jan;101(1-1):013102. doi: 10.1103/PhysRevE.101.013102.
We present a framework for performing input-output system identification near a Hopf bifurcation using data from only the fixed-point branch, prior to the Hopf point itself. The framework models the system with a van der Pol-type equation perturbed by additive noise, and identifies the system parameters via the corresponding Fokker-Planck equation. We demonstrate the framework on a prototypical thermoacoustic oscillator (a flame-driven Rijke tube) undergoing a supercritical Hopf bifurcation. We find that the framework can accurately predict the properties of the Hopf bifurcation and the limit cycle beyond it. This study constitutes an experimental demonstration of system identification on a reacting flow using only prebifurcation data, opening up pathways to the development of early warning indicators for nonlinear dynamical systems near a Hopf bifurcation.
我们提出了一个框架，用于在霍普夫分岔点之前仅使用来自定点分支的数据，在霍普夫分岔附近执行输入-输出系统识别。该框架用受加性噪声扰动的范德波尔型方程对系统进行建模，并通过相应的福克-普朗克方程识别系统参数。我们在一个经历超临界霍普夫分岔的典型热声振荡器（火焰驱动的里吉克管）上演示了该框架。我们发现该框架可以准确预测霍普夫分岔的特性及其后的极限环。这项研究构成了仅使用分岔前数据对反应流进行系统识别的实验演示，为开发霍普夫分岔附近非线性动力系统的早期预警指标开辟了道路。
