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Abstract
Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields.
Highlights
Many critical infrastructure and supply systems are based on structures which can be described in terms of complex networks [1,2,3,4,5,6]
In this study we investigate the collective dynamics of power grids which can serve as prototypical examples of critical infrastructure systems [26,27,28,29]
For Dw = 10.0 the survivability of inner tree nodes is strongly correlated with their basin stability which explains the occurring down-peaks
Summary
Many critical infrastructure and supply systems (e.g., transportation, health care or power supply) are based on structures which can be described in terms of complex networks [1,2,3,4,5,6]. Such real-world systems often evolved for the primary goal of fulfilling a specific function while subject to certain constraints (e.g., financing or geography). A still open question in this context is how the stability and resilience of networked systems is interrelated with their topological properties. While there are data-based approaches aiming at reconstructing network topology or complex dynamics (e.g., [11]), this study pursues a model-based approach aiming at rather qualitative insights into this interrelation
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