Description

• Title:
  Periodic solutions of vdP and vdP-like systems on 3-Tori
• Creator:
  Balanov, Zalman;
  Hooton, Edward;
  Murza, Adrian
• Description:
  Van der Pol equation (in short, vdP) as well as many its non-symmetric generalizations (the so-called van der Pol-like oscillators (in short, vdPl)) serve as nodes in coupled networks modeling real-life phenomena. Symmetric properties of periodic regimes of networks of vdP/vdPl depend on symmetries of coupling. In this paper, we consider $N^3$ identical vdP/vdPl oscillators arranged in a cubical lattice, where opposite faces are identified in the same way as for a $3$-torus. Depending on which nodes impact the dynamics of a given node, we distinguish between $\mathbb D_N \times \mathbb D_N \times \mathbb D_N$-equivariant systems and their $\mathbb Z_N \times \mathbb Z_N \times \mathbb Z_N$-equivariant counterparts. In both settings, the local equivariant Hopf bifurcation together with the global existence of periodic solutions with prescribed period and symmetry, are studied. The methods used in the paper are based on the results rooted in both equivariant degree theory and (equivariant) singularity theory.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.08.19
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 50, No 1 (September 2017); 253 - 268;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.023/12632 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.023/12633
• Subject:
  Equivariant Hopf bifurcation;
  coupled vdP oscillator;
  existence of periodic solutions;
  Primary;
  37G40;
  Secondary;
  34C25
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.023
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other