4 papers
Characteristic Operators and Spectral Properties of Periodic Evolutionary Systems
Bram Lentjes, Babette A. J. de Wolff
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we…
Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation
Christian Bick, Bob W. Rink, Babette A. J. de Wolff
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewr…
Validated error bounds for pseudospectral approximation of delay differential equations: unstable manifolds
Shane Kepley, Babette A. J. de Wolff
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a co…
Higher-order phase reduction captures delay-dependent synchronization phenomena in physical oscillator networks
Christian Bick, Bob Rink, Sagnik Chakraborty +3
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional pha…