---
_id: '33265'
abstract:
- lang: eng
  text: "This thesis deals with the investigation of dynamical properties – in particular
    generic synchrony breaking bifurcations – that are inherent to the structure of
    a semigroup network as well the numerous algebraic structures that are related
    to these types of networks. Most notably we investigate the interplay between
    network dynamics and monoid representation theory as induced by the fundamental
    network construction in terms of hidden symmetry as introduced by RINK and SANDERS.\r\n\r\nAfter
    providing a brief survey of the field of network dynamics in Part I, we thoroughly
    introduce the formalism of semigroup networks, the customized dynamical systems
    theory, and the necessary background from monoid representation theory in Chapters
    3 and 4. The remainder of Part II investigates generic synchrony breaking bifurcations
    and contains three major results. The first is Theorem 5.11, which shows that
    generic symmetry breaking steady state bifurcations in monoid equivariant dynamics
    occur along absolutely indecomposable subrepresentations – a natural generalization
    of the corresponding statement for group equivariant dynamics. Then Theorem 7.12
    relates the decomposition of a representation given by a network with high-dimensional
    internal phase spaces to that induced by the same network with one-dimensional
    internal phase spaces. This result is used to show that there is a smallest dimension
    of internal dynamics in which all generic l-parameter bifurcations of a fundamental
    network can be observed (Theorem 7.24).\r\n\r\nIn Part III, we employ the machinery
    that was summarized and further developed in Part II to feedforward networks.
    We propose a general definition of this structural feature of a network and show
    that it can equivalently be characterized in different algebraic notions in Theorem
    8.35. These are then exploited to fully classify the corresponding monoid representation
    for any feedforward network and to classify generic synchrony breaking steady
    state bifurcations with one- or highdimensional internal dynamics."
author:
- first_name: Sören
  full_name: Schwenker, Sören
  id: '97359'
  last_name: Schwenker
  orcid: 0000-0002-8054-2058
citation:
  ama: Schwenker S. <i>Genericity in Network Dynamics</i>. Universität Hamburg; 2019.
  apa: Schwenker, S. (2019). <i>Genericity in Network Dynamics</i>. Universität Hamburg.
  bibtex: '@book{Schwenker_2019, place={Hamburg}, title={Genericity in Network Dynamics},
    publisher={Universität Hamburg}, author={Schwenker, Sören}, year={2019} }'
  chicago: 'Schwenker, Sören. <i>Genericity in Network Dynamics</i>. Hamburg: Universität
    Hamburg, 2019.'
  ieee: 'S. Schwenker, <i>Genericity in Network Dynamics</i>. Hamburg: Universität
    Hamburg, 2019.'
  mla: Schwenker, Sören. <i>Genericity in Network Dynamics</i>. Universität Hamburg,
    2019.
  short: S. Schwenker, Genericity in Network Dynamics, Universität Hamburg, Hamburg,
    2019.
date_created: 2022-09-06T11:41:13Z
date_updated: 2022-09-07T08:32:14Z
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://ediss.sub.uni-hamburg.de/handle/ediss/6159
oa: '1'
place: Hamburg
publisher: Universität Hamburg
status: public
supervisor:
- first_name: Reiner
  full_name: Lauterbach, Reiner
  last_name: Lauterbach
title: Genericity in Network Dynamics
type: dissertation
user_id: '97359'
year: '2019'
...