The transition from the low-amplitude, aperiodic fluctuation to thermoacoustic instability is usually treated as a Hopf bifurcation, but the transition incorporates complex dynamical behaviors. Intermittent oscillations commonly occur in the transition process wherein chaotic states alternate with limit cycle oscillations and both the chaotic state and the limit cycle oscillation last with no fixed period. Intermittent oscillations that occur in the thermoacoustic system are demonstrated to be deterministic. A Koopman linearization procedure is implemented to model the intermittent combustion oscillations in the backward-facing step combustor. The nonlinear dynamics of intermittent combustion oscillations are approximated as a forced linear system in an orthogonal space, which is constructed by singular value decomposition of a delay coordinates matrix. The phase space of an intermittent combustion oscillation can be divided into linear and nonlinear regions by the magnitude of the nonlinear term in the forced linear system. As a result, intermittent combustion oscillations can be described as the transition between chaotic states and limit cycle oscillations, and the transition occurs when the nonlinear term is large.

从低振幅、非周期性波动到热声不稳定性的转变通常被视为 Hopf 分岔，但这种转变包含了复杂的动力学行为。过渡过程中通常会出现间歇性振荡，其中混沌状态与极限环振荡交替出现，并且混沌状态和极限环振荡都没有固定的周期。热声系统中发生的间歇性振荡被证明是确定性的。实施 Koopman 线性化程序来模拟后向阶梯式燃烧器中的间歇燃烧振荡。间歇燃烧振荡的非线性动力学近似为正交空间中的强制线性系统，它由延迟坐标矩阵的奇异值分解构成。根据受迫线性系统中非线性项的大小，间歇燃烧振荡的相空间可以分为线性区和非线性区。因此，间歇燃烧振荡可描述为混沌状态和极限循环振荡之间的过渡，当非线性项较大时发生过渡。