Sugitani Yoshiki, Kawahara Kensei, Konishi Keiji
Department of Electrical and Electronic Systems Engineering, <a href="https://ror.org/01hvx5h04">Osaka Metropolitan University</a>, 1-1 Gakuen, Naka-ku, Sakai, Osaka 599-8531, Japan.
Department of Electrical and Information Systems, <a href="https://ror.org/04s6fbg51">Osaka Prefecture University</a>, 1-1 Gakuen, Naka-ku, Sakai, Osaka 599-8531, Japan.
Phys Rev E. 2024 Jun;109(6-1):064213. doi: 10.1103/PhysRevE.109.064213.
Amplitude death has the potential to suppress unwanted oscillations in various engineering applications. However, in some engineering applications, such as dc microgrids, airfoil systems, and thermoacoustic systems, oscillation frequency is highly susceptible to external influences, leading to considerable variations. To maintain amplitude death amidst these frequency variations, we propose a design procedure that is robust against frequency variation for inducing amplitude death in delay-coupled oscillators. We first analytically derive the oscillator frequency band in which amplitude death can occur. The frequency bandwidth is maximized when the coupling strength is inversely proportional to the connection delay. Furthermore, our analysis reveals that the oscillator frequency band is influenced by the minimum eigenvalue of the normalized adjacency matrix (i.e., network topology) and that bipartite networks exhibit limited robustness to frequency variations. Our design procedure maintains the stability of amplitude death even under substantial frequency variations and is applicable to various network topologies. Numerical simulations confirm the validity of the proposed design.
振幅死亡有潜力抑制各种工程应用中不需要的振荡。然而，在一些工程应用中，如直流微电网、翼型系统和热声系统，振荡频率极易受到外部影响，导致显著变化。为了在这些频率变化中维持振幅死亡，我们提出了一种设计方法，该方法对于延迟耦合振荡器中诱导振幅死亡的频率变化具有鲁棒性。我们首先通过分析得出能够发生振幅死亡的振荡器频带。当耦合强度与连接延迟成反比时，频率带宽最大。此外，我们的分析表明，振荡器频带受归一化邻接矩阵的最小特征值（即网络拓扑）影响，并且二分网络对频率变化的鲁棒性有限。我们的设计方法即使在频率大幅变化的情况下也能维持振幅死亡的稳定性，并且适用于各种网络拓扑。数值模拟证实了所提设计的有效性。
