11 citations · 35 across the 8 of their papers we have counts for
4 papers · 1 filter
Phase Locking in Oscillator Networks with Uncertain and State-Dependent Couplings
Iva Bačić, Philipp C. Böttcher, Marc Hunkemöller +4
Phase locking in oscillator networks depends critically on the interaction strengths between coupled units. In many applications, however, these couplings are uncertain, state depe…
Linear Approximations Provide Rigorous Conditions for Phase Locking in Oscillator Networks and Power Grids
Iva Bačić, Carsten Hartmann, Philipp C. Böttcher +3
Synchronization is a fundamental collective phenomenon in many natural and engineered networks. The stable operation of oscillator networks, such as electric power grids, requires…
Local versus global stability in dynamical systems with consecutive Hopf-Bifurcations
Philipp C. Böttcher, Benjamin Schäfer, Stefan Kettemann +2
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response t…
Dynamic stability of electric power grids: Tracking the interplay of the network structure, transmission losses and voltage dynamics
Philipp C. Böttcher, Dirk Witthaut, Leonardo Rydin Gorjão
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay…