32 citations · 59 across the 14 of their papers we have counts for
17 papers
Homogeneous coupled cell systems with high-dimensional internal dynamics
Sören von der Gracht, Eddie Nijholt, Bob Rink
The analysis of network dynamics is oftentimes restricted to networks with one-dimensional internal dynamics. Here, we show how symmetry explains the relation between behavior of s…
Dimension Bounds for Systems of Equations with Graph Structure
Eddie Nijholt, Davide Sclosa
We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension o…
Higher order interactions lead to "reluctant" synchrony breaking
Sören von der Gracht, Eddie Nijholt, Bob Rink
To model dynamical systems on networks with higher order (non-pairwise) interactions, we recently introduced a new class of ODEs on hypernetworks. Here we consider one-parameter sy…
Chaotic behavior in diffusively coupled systems
Eddie Nijholt, Tiago Pereira, Fernando C. Queiroz +1
We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a…
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…