arXiv subjects

Marc Hunkemöller

Publications and source records attributed to Marc Hunkemöller.

3 recordsLinked to original sources

arXiv2026

Phase Locking in Oscillator Networks with Uncertain and State-Dependent Couplings

Phase locking in oscillator networks depends critically on the interaction strengths between coupled units. In many applications, however, these couplings are uncertain, state dependent, or time varying. We derive rigorous conditions for phase locking in Kuramoto-type networks when each coupling strength is known only within prescribed bounds. Building on a convex formulation of the nonlinear fixed-point equations, we obtain edge-wise error bounds for arbitrary feasible approximations that hold uniformly over all admissible couplings. These bounds yield sufficient conditions for the existence of phase-locked states with prescribed phase-difference limits. We illustrate the framework for AC power grids with uncertain voltage magnitudes and adaptive oscillator networks with state-dependent couplings. For the latter, the bounds can be further tightened by exploiting the state dependence of the couplings.

nlin.AO↗

arXiv2026

Low-rank corrections to a shared reference Jacobian for GPU-parallel AC $N\!-\!1$ contingency analysis

Contingency analysis repeatedly solves the power-flow equations under many single-element outages, an increasingly demanding workload as operating margins tighten and renewable variability grows. Graphics processing units (GPUs) are attractive for this task, but a change in topology alters the sparsity pattern of the Jacobian, preventing the uniform batched factorization on which efficient GPU solvers rely. This paper presents a GPU-parallel Newton--Raphson solver for $N\!-\!1$ contingency analysis that separates the change in operating state from the change in topology. A single reference Jacobian is inverted once and reused across all contingencies. Each topology change is expressed as a low-rank Woodbury correction, while the residual state-dependent perturbation is handled by an inner iterative solve, a truncated Neumann series or the biconjugate gradient stabilized method. We analyze the spectral radius and condition number of the resulting iteration matrices and show that the reference Jacobian is an effective preconditioner. On transmission-scale benchmarks, the method attains per-topology solve times competitive with an optimized 80-core central processing unit baseline, with the low-rank correction accounting for approximately 1--2\% of the workload. This makes GPU-parallel $N\!-\!1$ contingency analysis feasible at transmission scale without per-topology refactorization.

eess.SY↗

arXiv2026

Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities

We theoretically investigate how phase modulation alters the dynamics of temporal localized structures (TLSs) in vertically emitting Kerr micro-cavities under detuned optical injection operating in the normal dispersion regime. We show that the emergence of TLSs in general is governed by a synchronization between the imposed modulation and the intrinsic pulse dynamics. We perform a multi-parameter bifurcation analysis of the underlying delay-algebraic equation model in the uniform field limit and demonstrate that weakly nonlinear and dissipative Hermite-Gauss modes shape the dynamics of dark TLSs, leading to a complex hybrid bifurcation structure. Beyond the uniform field limit, both bright and dark modulated TLSs are shown to exist and to occupy distinct equilibrium positions within the cavity. An effective equation of motion for the TLS positions is derived, showing a good agreement with the full model.

nlin.PS↗