The occurrence of synchronization and amplitude death phenomena due to the coupled interaction of limit cycle oscillators (LCO) has received increased attention over the last few decades in various fields of science and engineering. Studies pertaining to these coupled oscillators are often performed by studying the effect of various coupling parameters on their mutual interaction. However, the effect of system parameters (i.e., the amplitude and frequency) on the coupled interaction of such LCO has not yet received much attention, despite their practical importance. In this paper, we investigate the dynamical behavior of time-delay coupled Stuart–Landau (SL) oscillators exhibiting subcritical Hopf bifurcation for the variation of amplitude and frequency of these oscillators in their uncoupled state. For identical SL oscillators, a gradual increase in the amplitude of LCO shrinks the amplitude death regions observed between the regions of in-phase and anti-phase synchronization leading to its eventual disappearance, resulting in the occurrence of phase-flip bifurcations at higher amplitudes of LCO. We also observe an alternate existence of in-phase and anti-phase synchronization regions for higher values of time delay, whose prevalence of occurrence increases with an increase in the frequency of the oscillator. With the introduction of frequency mismatch, the region of amplitude death. The forced response of SL oscillator shows an asymmetry in the Arnold tongue and the manifestation of asynchronous quenching of LCO. An increase in the amplitude of LCO narrows the Arnold tongue and reduces the region of asynchronous quenching observed in the system. Finally, we compare the coupled and forced response of SL oscillators with the corresponding experimental results obtained from laminar thermoacoustic oscillators and the numerical results from van der Pol (VDP) oscillators. We show that the SL model qualitatively displays many features observed experimentally in coupled and forced thermoacoustic oscillators. In contrast, the VDP model does not capture most of the experimental results due to the limitation in the independent variation of system parameters.

在过去的几十年中，由于极限循环振荡器（LCO）的耦合相互作用而导致的同步和振幅消失现象的出现，在科学和工程学的各个领域中引起了越来越多的关注。关于这些耦合振荡器的研究通常是通过研究各种耦合参数对其相互作用的影响来进行的。然而，尽管系统参数（即幅度和频率）对这种LCO的耦合相互作用的影响具有实际意义，但尚未引起足够的重视。在本文中，我们研究了时延耦合Stuart-Landau（SL）振荡器的动力学行为，这些振荡器在未耦合状态下表现出次临界Hopf分叉，从而改变了这些振荡器的幅度和频率。对于相同的SL振荡器，LCO振幅的逐渐增加使在同相和反相同步区域之间观察到的振幅死亡区域缩小，最终导致其消失，从而导致在LCO振幅较高时发生相翻转分叉。我们还观察到同相和反相同步区域存在较高的时间延迟值，该频率的发生率随着振荡器频率的增加而增加。随着频率失配的引入，振幅区域消失。SL振荡器的强制响应在Arnold舌中显示出不对称性，并表现出LCO的异步淬火。LCO幅度的增加使Arnold舌头变窄，并减小了系统中观察到的异步淬火区域。最后，我们将SL振荡器的耦合响应和强迫响应与层流热声振荡器的相应实验结果以及van der Pol（VDP）振荡器的数值结果进行了比较。我们显示SL模型定性显示了耦合和强制热声振荡器实验观察到的许多功能。相反，由于系统参数独立变化的限制，VDP模型无法捕获大多数实验结果。