100 citations · 316 across the 24 of their papers we have counts for
26 papers
A parametrisation method for high-order phase reduction in coupled oscillator networks
Sören von der Gracht, Eddie Nijholt, Bob Rink
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)perio…
Hypernetworks: cluster synchronisation is a higher-order effect
Sören von der Gracht, Eddie Nijholt, Bob Rink
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In…
Amplified steady state bifurcations in feedforward networks
Sören von der Gracht, Eddie Nijholt, Bob Rink
We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this proper…
Korteweg-de Vries and Fermi-Pasta-Ulam-Tsingou: asymptotic integrability of quasi unidirectional waves
Matteo Gallone, Antonio Ponno, Bob Rink
In this paper we construct a higher order expansion of the manifold of quasi unidirectional waves in the Fermi-Pasta-Ulam (FPU) chain. We also approximate the dynamics on this mani…
Multiple timescales and the parametrisation method in geometric singular perturbation theory
Ian Lizarraga, Bob Rink, Martin Wechselberger
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by t…
Quiver representations and dimension reduction in dynamical systems
Eddie Nijholt, Soeren Schwenker, Bob Rink
Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quive…