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A Hopf bifurcation is prevalent in many nonlinear dynamical systems. When asystem prior to a Hopf bifurcation is exposed to a sufficient level of noise,its noise-induced dynamics can provide valuable information about the impendingbifurcation. In this thesis, we present a system identification (SI) frameworkthat exploits the noise-induced dynamics prior to a Hopf bifurcation. Theframework is novel in that it is capable of predicting the bifurcation pointand the post-bifurcation dynamics using only pre-bifurcation data.Specifically, we present two different versions of the framework: input-outputand output-only. For the input-output version, the system is forced withadditive noise generated by an external actuator, and its response is measured.For the output-only version, the intrinsic noise of the system acts as thenoise source and only the output signal is measured. In both versions, theFokker-Planck equations, which describe the probability density function of thefluctuation amplitude, are derived from self-excited oscillator models. Then,the coefficients of these models are extracted from the experimentalprobability density functions characterizing the noise-induced response in thefixed-point regime. The SI framework is tested on three different experimentalsystems: a low-density jet, a flame-driven Rijke tube, and a gas-turbinecombustor. For these systems, we demonstrate that the proposed framework canidentify the nature of the Hopf bifurcation and the system's order ofnonlinearity. Moreover, by extrapolating the identified model coefficients, weare able to forecast the locations of the bifurcation points and thelimit-cycle features after those points. To the best of our knowledge, this isthe first time that SI has been performed using data from only thepre-bifurcation regime, without the need for knowledge of the location of thebifurcation point.

System Identification near a Hopf Bifurcation via the Noise-Induced Dynamics in the Fixed-Point Regime