Punetha Nirmal, Wetzel Lucas
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Amity University Haryana, Gurugram (Manesar), 122413 Haryana, India.
Phys Rev E. 2022 Nov;106(5):L052201. doi: 10.1103/PhysRevE.106.L052201.
We study synchronization in networks of delay-coupled electronic oscillators, so-called phase-locked loops (PLLs). Using a phase-model description, we study the collective dynamics of mutually coupled PLLs and report the phenomenon of heterogeneity-induced synchronization. This phenomenon refers to the observation that heterogeneity in the system's parameters can induce synchronization by stabilizing the states which are unstable without such heterogeneity. In systems where component heterogeneity can be tuned and controlled, we show how the complex collective self-organized dynamics can be guided towards synchronized states with specific operational frequencies and phase relations. This is of importance for the technical applicability of self-organized dynamics. In electrical engineering, for example, where components can be strongly heterogeneous, our theoretical framework can inform the design process for networks of spatially distributed PLLs. The results presented here are also useful in understanding the collective dynamics in ensembles of phase oscillators with time-delayed interactions, inertia, and heterogeneity.
我们研究延迟耦合电子振荡器网络中的同步现象，即所谓的锁相环（PLL）。通过相位模型描述，我们研究了相互耦合的锁相环的集体动力学，并报告了异质性诱导同步的现象。这种现象指的是观察到系统参数中的异质性可以通过稳定在没有这种异质性时不稳定的状态来诱导同步。在组件异质性可以被调整和控制的系统中，我们展示了复杂的集体自组织动力学如何能够被引导到具有特定工作频率和相位关系的同步状态。这对于自组织动力学的技术适用性很重要。例如，在电气工程中，组件可能具有很强的异质性，我们的理论框架可以为空间分布的锁相环网络的设计过程提供参考。这里呈现的结果对于理解具有时间延迟相互作用、惯性和异质性的相位振荡器集合中的集体动力学也很有用。
