Description

• Title:
  A periodic bifurcation problem depending on a random variable
• Creator:
  Kamenskiĭ, Mikhail I.;
  Nistri, Paolo;
  de Fitte, Paul Raynaud
• Description:
  We consider an abstract bifurcation equation $P(x)+\varepsilon Q(x,\varepsilon, \omega)=0$, where $P$ and $Q$ are operators, $\varepsilon$ is the bifurcation parameter, $\omega \in \Omega$, is the random variable and $(\Omega, \mathcal{F})$ is a measurable space. The aim of the paper is to provide conditions on $P$ and $Q$ to ensure the existence, for any $\omega \in \Omega$, of a branch of solutions originating from the zeros of the operator $P$. We show that the considered abstract bifurcation is the model of a random autonomous periodically perturbed differential equation having the property that the unperturbed equation corresponding to $\varepsilon = 0$ has a limit cycle. As a consequence we obtain the existence, for any $\omega \in \Omega$, of a branch of periodic solutions of the perturbed equation emanating from the limit cycle.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.27
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2B (December 2019); 979 - 999;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.043/18041 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.043/18042
• Subject:
  Random variable;
  Malkin bifurcation function;
  limit cycle;
  periodic perturbation;
  Primary;
  37G15;
  Secondary;
  34F05 34F10 34C25}
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.043
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other