16 citations · 59 across the 17 of their papers we have counts for
9 papers · 1 filter
The Lie algebraic structure of colored networks
Fahimeh Mokhtari, Jan Sanders
In the computation of the normal form of a colored network vector field, following the semigroup(oid) approach in [19], one would like to be able to say something about the structu…
Vector potential normal form classification for completely integrable solenoidal nilpotent singularities
Majid Gazor, Fahimeh Mokhtari, Jan A. Sanders
We introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form…
Projection blocks in homogeneous coupled cell networks
Eddie Nijholt, Bob Rink, Jan Sanders
We introduce a special subset of the graph of a homogeneous coupled cell network, called a projection block, and show that the network obtained from identifying this block to a sin…
Center manifolds of coupled cell networks
Eddie Nijholt, Bob Rink, Jan Sanders
Dynamical systems with a network structure can display anomalous bifurcations as a generic phenomenon. As an explanation for this it has been noted that homogeneous networks can be…
Graph fibrations and symmetries of network dynamics
Eddie Nijholt, Bob Rink, Jan Sanders
Dynamical systems with a network structure can display collective behaviour such as synchronisation. Golubitsky and Stewart observed that all the robustly synchronous dynamics of a…
Coupled cell networks and their hidden symmetries
Bob Rink, Jan Sanders
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here…