论文标题
偶尔耦合会增强延迟耦合振荡器中的振幅死亡
Occasional coupling enhances amplitude death in delay-coupled oscillators
论文作者
论文摘要
本文旨在使用偶尔的耦合方案研究振幅死亡,以时延迟耦合振荡器,这意味着振荡器之间的间歇相互作用。使用一对延迟耦合振荡器中的偶尔耦合,可以使用振幅死亡区域的增强(即沿控制参数轴的宽度的增量)。我们的研究始于耦合极限周期振荡器(Stuart-Landau)和混沌振荡器(Rössler)。我们进一步检查了耦合的水平rijke管,这是热声系统的原型模型。振荡状态对热声系统(例如燃烧器)高度有害。因此,总是首选振幅死亡的状态。我们将启用耦合(即平方波函数)作为偶尔的耦合方案(即偶尔的耦合方案)。在单调改变耦合强度(作为对照参数)时,我们观察到与连续耦合方案相比,使用偶尔的耦合方案来增强振幅死亡区域的增强。为了研究偶尔耦合方案的贡献,我们进行了详细的线性稳定性分析,并通过分析解释了耦合极限周期振荡器的振幅死亡区域的增强。我们还采用振荡器的频率比和振荡器之间的时间延迟作为控制参数。有趣的是,我们使用频率比和时间延迟作为偶尔耦合的控制参数获得了振幅死亡区域的类似增强。最后,我们使用半波整流的正弦波函数(由实际现实动机)来引入偶尔的时间耦合振荡器,并获得相似的结果。
This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies the intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart-Landau) and coupled chaotic oscillators (Rössler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on-off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time-delay coupled oscillators and get similar results.