7 citations · 19 across the 8 of their papers we have counts for
8 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…
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…
Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions
Christian Bick, Sören von der Gracht
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which…
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…
On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies
Raphael Gerlach, Sören von der Gracht, Michael Dellnitz
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed num…
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…
Equivariant Bifurcation and Absolute Irreducibility in A contribution to the Ize conjecture
Reiner Lauterbach
M. Field [5] refers to an unpublished work by J. Ize for a result that loss of stability through an absolutely irreducible representation of a compact Lie group leads to bifurcatio…