Quenching of limit-cycle oscillations (LCOs), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in quenching of LCOs has rarely been studied despite its practical applicability. We study the dynamics of two thermoacoustic oscillators simultaneously subjected to mutual coupling and asymmetric external forcing through experiments and theoretical modeling. We investigate the forced response of both identical and nonidentical thermoacoustic oscillators for two different amplitudes of LCOs. Under mutual coupling alone, identical thermoacoustic oscillators display the occurrence of partial amplitude death and amplitude death, whereas under forcing alone, asynchronous quenching of LCOs is observed at nonresonant conditions. When the oscillators are simultaneously subjected to mutual coupling and asymmetric forcing, we observe a larger parametric region of oscillation quenching than when the two mechanisms are utilized individually. This enhancement in the region of oscillation quenching is due to the complementary effect of amplitude death and asynchronous quenching. However, the forced response of coupled nonidentical oscillators shows that the effect of forcing is insignificant on attaining synchronization and quenching of oscillations in the oscillator that is not directly forced. Finally, we qualitatively capture the experimental results using a reduced-order theoretical model of two Rijke tubes that are coupled through dissipative and time-delay coupling and asymmetrically forced. We believe that these findings offer fresh insights into the combined effects of mutual and forced synchronization in a system of coupled nonlinear oscillators.

中文翻译：

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非对称强迫作用下耦合热声振荡器的动力学

通过相互耦合或外部强迫进行的极限循环振荡（LCO）的淬灭在科学和工程学的多个领域中引起了广泛的关注。然而，尽管其实际适用性，但很少研究在LCO淬灭中同时利用这些偶联方案。通过实验和理论模型，我们研究了两个同时经历相互耦合和不对称外力作用的热声振荡器的动力学。我们研究了两种不同幅度的LCO的相同和不同的热声振荡器的强制响应。仅在相互耦合的情况下，相同的热声振荡器会显示出部分振幅衰减和振幅衰减的发生，而在单独施加力的情况下，在非共振条件下观察到LCO的异步猝灭。当振荡器同时受到相互耦合和非对称作用力时，与两个机构分别使用时相比，我们观察到更大的参数范围的振荡猝灭。振荡猝灭区域的这种增强归因于振幅下降和异步猝灭的互补作用。但是，耦合的不同振荡器的强制响应表明，强制作用对于在未直接强制的振荡器中实现同步和抑制振荡的作用微不足道。最后，我们使用两个Rijke管的降阶理论模型定性地捕获了实验结果，这两个Rijke管通过耗散和时滞耦合进行耦合，并且受到非对称作用。