2017
DOI: 10.1088/1367-2630/aa6321
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Deciphering the imprint of topology on nonlinear dynamical network stability

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 … Show more

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Cited by 38 publications
(63 citation statements)
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“…5) Random Triangle Networks: Triangular structure, which has been observed benefit to the robustness of controllability [17] and network stability [53], [54], is frequently observed in real-life situations.…”
Section: Experimental Studiesmentioning
confidence: 99%
“…5) Random Triangle Networks: Triangular structure, which has been observed benefit to the robustness of controllability [17] and network stability [53], [54], is frequently observed in real-life situations.…”
Section: Experimental Studiesmentioning
confidence: 99%
“…This conclusion is valid for the reduced systems of equations (6) and (8)(9) which approximate the full network. In the realm of AC power grids, there is a profusion of attractors, including anomalous ones that can not be understood in the reduced way 10 . However, during all numerical tests involving a wide range of parameters no other stable attractors than those denoted above with P + or P (normal operation) and the collapse X have ever been observed, so it appears that this is not the case for the DC system.…”
Section: Perturbation At a Producer Nodementioning
confidence: 99%
“…Subsequent works refined this in many direction, e.g. by identifying specific topological structures that trigger the existence of accessible new limit cycles 10 .…”
Section: Introductionmentioning
confidence: 99%
“…The bistability of power-grid nodes is also analyzed over the state space of nodes 4,5 . Based on the transient pattern in the state space, different categories of the power-grid nodes in terms of topological roles are analyzed to show their distinct diagnostics in the basin stability 6 . From a practical point of view, numerical studies on basin stability require heavy computational resources due to its time complexity in exploring the state space, so modified versions were developed to estimate the basin stability 7 and sometimes with setting the finite-time limit 51,52 .…”
Section: The Synchronization Stabilitymentioning
confidence: 99%