A van der Pol-Duffing Oscillator with Indefinite Degree

• Hebai Chen ^[1] ; Jie Jin ^[1] ; Zhaoxia Wang ^[2] ; Baodong Zhang ^[1]
  1. [1] Central South University

     Central South University

     China

     
  2. [2] University of Electronic Science and Technology of China

     University of Electronic Science and Technology of China

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • This paper is to study the global dynamics of a van der Pol-Duffing oscillator with indefinite degree x˙ = y, y˙ = ax+x2n+1−δ(b+x2m)y, where a, b, δ ∈ R, m, n ∈ N+ and δ = 0. By qualitative and bifurcation analysis, the oscillator contains abundant nonlinear phenomena, including the heteroclinic bifurcation, degenerate Hopf bifurcation, bifurcation of equilibria at infinity and pitchfork bifurcation.