Bera Bidesh K
Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel.
Chaos. 2020 Feb;30(2):023132. doi: 10.1063/1.5130543.
In this paper, we investigate the dynamical robustness of diffusively coupled oscillatory networks under the influence of an additional repulsive link. Such a dynamical resilience property is realized through the aging process of the damaged network of active and inactive oscillators. The aging process is one type of phase transition, mainly appearing at a critical threshold of a fraction of the inactive oscillator node where the mean oscillation amplitude of the entire network suddenly vanishes. These critical fractions of the failure nodes in the network are broadly used as a measure of network resilience. Here, we analytically derived the critical fraction of the aging process in the dynamical network. We find that the addition of the repulsive link enhances the critical threshold of the aging transition of diffusively coupled oscillators, which indicated that the dynamical robustness of the coupled network decreases with the presence of the repulsive interaction. Furthermore, we investigate the dynamical robustness of the network against the number of deteriorating repulsive links. We observed that a certain percentage of the repulsive link is enabled to produce the aging process in the entire network. Finally, the effect of symmetry-breaking coupling and the targeted inactivation process on the dynamical robustness property of damaged networks were investigated. The analytically obtained results are verified numerically in the network of coupled Stuart-Landau oscillators. These findings may help us to better understand the role of the coupling mechanism on the phase transition in the damaged network.
在本文中，我们研究了在附加排斥链路影响下扩散耦合振荡网络的动力学鲁棒性。这种动力学弹性特性是通过有源和无源振荡器的受损网络的老化过程实现的。老化过程是一种相变类型，主要出现在无源振荡器节点比例的临界阈值处，此时整个网络的平均振荡幅度突然消失。网络中故障节点的这些临界比例被广泛用作网络弹性的度量。在这里，我们通过分析得出了动态网络中老化过程的临界比例。我们发现，排斥链路的添加提高了扩散耦合振荡器老化转变的临界阈值，这表明耦合网络的动力学鲁棒性随着排斥相互作用的存在而降低。此外，我们研究了网络针对恶化的排斥链路数量的动力学鲁棒性。我们观察到，一定比例的排斥链路能够在整个网络中产生老化过程。最后，研究了对称破缺耦合和靶向失活过程对受损网络动力学鲁棒性特性的影响。在耦合的斯图尔特 - 兰道振荡器网络中对分析得到的结果进行了数值验证。这些发现可能有助于我们更好地理解耦合机制在受损网络相变中的作用。
