What adaptive neuronal networks teach us about power grids

Abstract

Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the last decade. In this paper, we provide insight into the fundamental relation between these two types of networks. For this, we consider well-established models based on phase oscillators and show their intimate relation. In particular, we prove that phase oscillator models with inertia can be viewed as a particular class of adaptive networks. This relation holds even for more general classes of power grid models that include voltage dynamics. As an immediate consequence of this relation, we find a novel type of multicluster state for phase oscillators with inertia. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network.

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Cited by in corpus (12)

• Perspectives on adaptive dynamical systems
• Heterogeneous nucleation in finite size adaptive dynamical networks
• Generalized splay states in phase oscillator networks
• Transition from chimera/solitary states to traveling waves
• Synchronization transitions in Kuramoto networks with higher-mode interaction
• Global topological synchronization of weighted simplicial complexes
• Mixed-Mode Chimera states in Pendula Networks
• Complex Couplings -- A universal, adaptive and bilinear formulation of power grid dynamics
• Resonant Solitary States in Complex Networks
• Modelling power grids as pseudo adaptive networks
• Origin of Frequency Clusters and Self-Organized Triplet Locking in the Kuramoto Model with Inertia
• Emergence of solitary and chimera states in adaptive pendulum networks under diverse learning rules