Quiver representations and dimension reduction in dynamical systems

Eddie Nijholt, Bob W. Rink, Sören Schwenker

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Dynamical systems often admit geometric properties that must be taken into account when studying their behavior. We show that many such properties can be encoded by means of quiver representations. These properties include classical symmetry, hidden symmetry, and feedforward structure, as well as subnetwork and quotient relations in network dynamical systems. A quiver equivariant dynamical system consists of a collection of dynamical systems with maps between them that send solutions to solutions. We prove that such quiver structures are preserved under Lyapunov-Schmidt reduction, center manifold reduction, and normal form reduction.

Original languageEnglish
Pages (from-to)2428-2468
Number of pages41
JournalSIAM Journal on Applied Dynamical Systems
Issue number4
Early online date2 Nov 2020
Publication statusPublished - Dec 2020


  • Bifurcation theory
  • Coupled networks
  • Normal forms
  • Quiver representations
  • Symmetry


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