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Symmetric bifurcation analysis of synchronous states of time-delay oscillators networks.

Ferruzzo Correa, Diego Paolo

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Escola Politécnica 2014-05-30

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  • Title:
    Symmetric bifurcation analysis of synchronous states of time-delay oscillators networks.
  • Author: Ferruzzo Correa, Diego Paolo
  • Supervisor: Piqueira, José Roberto Castilho
  • Subjects: Bifurcações; Sistemas Com Atraso De Tempo; Equações Diferencias Com Atraso; Grupo De Lie; Simetria; Rede De Osciladores; Symmetry; Oscillator Network; Lie Group; Delay Differential Equations; Bifurcations; Time-Delay System
  • Notes: Tese (Doutorado)
  • Local notes: Programa Engenharia Elétrica
  • Description: In recent years, there has been increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order N-node time-delay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steady-state and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.
  • DOI: 10.11606/T.3.2014.tde-29122014-180651
  • Publisher: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Escola Politécnica
  • Creation Date: 2014-05-30
  • Format: Adobe PDF
  • Language: English
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