Description

• Title:
  On a class of polynomial differential systems of degree 4: phase portraits and limit cycles
• Creator:
  Llibre, Jaume;
  Salhi, Tayeb
• Description:
  In this paper we characterize the phase portraits in the Poincaré disc of the class of polynomial differential systems of the form \begin{equation*} \dot{x}=-y,\qquad \dot{y} =x+ax^{4}+bx^{2}y^{2}+cy^{4}, \end{equation*} with $a^2+b^2+c^2\neq0$, which are symmetric with respect to the $x$-axis. Such systems have a center at the origin of coordinates. Moreover, using the averaging theory of five order, we study the number of limit cycles which can bifurcate from the period annulus of this center when it is perturbed inside the class of all polynomial differential systems of degree $4$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.06.07
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 2 (June 2021); 441 - 463;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.042/29094 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.042/29095
• Subject:
  Polynomial differential systems;
  polynomial vector fields;
  phase portraits;
  centers;
  limit cycles;
  34C05;
  34A34
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.042
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other