[BOEK][B] Dynamics and bifurcation in networks: theory and applications of coupled differential equations

M Golubitsky, I Stewart - 2023 - SIAM
The biologist JBS Haldane, when asked what we can learn about the Creator by examining
the world, is said to have replied “an inordinate fondness for beetles”[705]. Today's …

The steady-state lifting bifurcation problem associated with the valency on networks

MAD Aguiar, APS Dias, P Soares - Physica D: Nonlinear Phenomena, 2019 - Elsevier
In this paper we consider homogeneous coupled cell networks with asymmetric inputs—
networks where each cell receives exactly one input of each edge type. The coupled cell …

An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks

PM Sequeira, JP Hespanha, AP Aguiar - Nonlinearity, 2023 - iopscience.iop.org
This paper presents an in-reachability based classification of invariant synchrony patterns in
coupled cell networks (CCNs). These patterns are encoded through partitions on the set of …

An overview of synchrony in coupled cell networks

MAD Aguiar, APS Dias - … , Optimization and Bioeconomics III: DGS IV …, 2018 - Springer
One of the key aspects in the theory of coupled cell networks concerns the existence of
synchrony subspaces. That is, subspaces defined in terms of equalities between cell …

Reduced lattices of synchrony subspaces and their indices

H Kamei, H Ruan - SIAM journal on applied dynamical systems, 2021 - SIAM
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces
that are invariant under the network adjacency matrix. The complete lattice of synchrony …

[PDF][PDF] An equivariant degree theory for networked dynamical systems

H Ruan - 2016 - math.uni-hamburg.de
We extend the scope of equivariant degree theory and methods to the realm of networked
dynamical systems. Focusing on two types of hidden symmetries of networked systems, we …